26 and 2026 in Numbers and Magic Squares

Inder J. Taneja https://numbers-magic.com; www.inderjtaneja.wordpress.com 26 and 2026 in Numbers and Magic Squares, Zenodo, December 22, 2025, pp. 1-74, https://doi.org/10.5281/zenodo.17944238 26 and 2026 in Numbers and Magic Squares Site link: https://numbers-magic.com/?p=17306 Inder J. Taneja1 Abstract This work brings different representations of 26 and 2026 in numbers and magics squares. The number representations are of crazy-type, pyramid-type, single-digit, single-letter, running expressions, Triangular, Fibonacci, palindromic-type, prime numbers, embedded prime patterns, selfie, semi-selfie, narcissistic, etc. Some interesting patterns for 26 and 2026 are also included in the work. The magic square representations are of types double-digit bordered,cornered,upsidedown, etc. condering magic sum as 26 and 2026. 1Formerly, Professor of Mathematics, Federal University of Santa Catarina, Florianópolis, SC, Brazil (1978-2012). E-mail: [email protected]; Web-sites: https://numbers-magic.com; https://inderjtaneja.wordpress.com; Twitter: @IJTANEJA; Instagram: @crazynumbers. 1 Inder J. Taneja https://numbers-magic.com; www.inderjtaneja.wordpress.com 26 and 2026 in Numbers and Magic Squares, Zenodo, December 22, 2025, pp. 1-74, https://doi.org/10.5281/zenodo.17944238 Contents 1 Upside-down and Mirror Looking Representations of 26 and 2026 6 1.1 Representationsof26 ....................................... 6 1.1.1 First-Type: Upside-down and Mirror Looking . . . . . . . . . . . . . . . . . . . . . 6 1.1.2 Second-Type: Upside-down and Mirror Looking . . . . . . . . . . . . . . . . . . . . 6 1.1.3 Third-Type:Upside-down................................. 6 1.2 Representationsof2026 ...................................... 6 1.2.1 First-Type: Upside-down and Mirror Looking . . . . . . . . . . . . . . . . . . . . . 7 1.2.2 Second-Type: Upside-down and Mirror Looking . . . . . . . . . . . . . . . . . . . . 7 1.2.3 Third-Type: Upside-down and Mirror Looking . . . . . . . . . . . . . . . . . . . . . 7 1.2.4 Forth-Type: Upside-down and Mirror Looking . . . . . . . . . . . . . . . . . . . . . 7 1.2.5 Fifth-Type:Upside-down ................................. 8 2 2026 in Magic Squares of Order 4 9 2.1 First-Way............................................... 9 2.2 Second-Way ............................................. 10 3 Crazy Representations 11 3.1 BasicOperations .......................................... 11 3.1.1 10 numbers 1, 2,... 10: Increasing and Decreasing . . . . . . . . . . . . . . . . . . . . 11 3.2 Factorial ............................................... 12 3.3 Square-Root ............................................. 12 3.4 SquareFunction........................................... 12 3.5 CubicFunction ........................................... 12 3.6 FibonacciSequence......................................... 13 3.7 TriangularNumbers ........................................ 13 4 Pyramid-Type Representations 13 5 Single Digit Representations 14 5.1 PatternsinSingleDigit....................................... 15 5.1.1 Pattern in Single Digit for 26 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 5.1.2 Pattern in Single Digit for 2026 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 6 Single Letter Representations 17 6.1 PatternsinSingleLetterfor26................................... 17 6.2 Patterns in Single Letter for 2026 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2 Inder J. Taneja https://numbers-magic.com; www.inderjtaneja.wordpress.com 26 and 2026 in Numbers and Magic Squares, Zenodo, December 22, 2025, pp. 1-74, https://doi.org/10.5281/zenodo.17944238 7 Running Equality Expressions for 26 18 7.1 FactorialandSquare-Root ..................................... 18 7.2 FibonacciSequenceValues..................................... 19 7.3 TriangularNumbers ........................................ 20 8 Pythagorean Triples 20 8.1 Pattern in Pythagorean Triples with 26 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 8.2 Pattern in Pythagorean Triples with 2026 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 9 Selfie Representations 21 10 Selfie Fractions for 26 and 2026 22 10.1SelfieFractionsfor26........................................ 22 10.2 Patterns in Selfie Fractions for 26 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 10.3SelfieFractionsfor2026 ...................................... 23 10.4 Patterns in Selfie Fractions for 2026 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 11 Equivalent Fractions 33 11.1EquivalentFractionsfor26..................................... 33 12 Narcissistic Type Representations 34 12.1 Narcissistic Type Representations for 26 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 12.2 Narcissistic Type Representations for 2026 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 13 Semi-Selfie Representations 34 13.1Powersof26............................................. 34 13.2Poweras26 ............................................. 35 14 Power Representations 35 14.1Powersof2.............................................. 35 14.2Power2................................................ 35 14.310000+2026:Power2 ........................................ 36 14.4PatternswithPowers3and4 ................................... 36 15 Square-Power Patterns 37 15.1Square-PowerPatternsfor26 ................................... 37 15.2 Square-Power Patterns for 2026 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 16 Power-Plus-Minus Equalities 38 16.1 Power-Plus-Minus Equalities for 26 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 16.2 Power-Plus-Minus Equalities for 2026 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 3 Inder J. Taneja https://numbers-magic.com; www.inderjtaneja.wordpress.com 26 and 2026 in Numbers and Magic Squares, Zenodo, December 22, 2025, pp. 1-74, https://doi.org/10.5281/zenodo.17944238 17 Factorial-Power Equalities 39 17.1 Factorial-Power Equalities for 26 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 18 Fibonacci-Triangular Equalities 40 18.1 Factorial-Fibonacci-Trianguar Equalities for 26 . . . . . . . . . . . . . . . . . . . . . . . . . 40 19 Representations of Numbers from 1 to 260 Terms of 2026-6202 42 20 Embedded Prime Patterns 46 20.1 Non Palindromic Prime Patterns for 2026 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 20.2 Palindromic Prime Patterns for 2026 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 21 Fixed Digits Repetitions Primes Patterns 48 21.1Length7 ............................................... 48 21.2Length8 ............................................... 50 22 Pattern in Multiplication and Division with 26 50 22.1Multiplication............................................ 50 22.2Division:Recurringnumbers ................................... 51 23 Palindromic-Type Patterns and Expressions 51 23.1 Palindromic-Type Patterns for 25 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 23.2 Palindromic-Type Patterns for 2026 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 23.3 Palindromic-Type Expressions for 26 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 23.4 Palindromic-Type Expressions for 2025 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 24 Color Patterns 55 24.1 Three Color Patterns for 12 Month of 2026 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 24.1.1 Months1and2....................................... 55 24.1.2 Months3and4....................................... 56 24.1.3 Months5and6....................................... 56 24.1.4 Months7and8....................................... 57 24.1.5 Months9and10 ...................................... 57 24.1.6 Months11and12...................................... 58 24.2TwoColorPatternsfor20-26.................................... 58 25 Magic Squares with Magic Sum 26 and 2026 61 25.1MagicSquaresofOrder3 ..................................... 61 25.2MagicSquaresofOrder4 ..................................... 62 25.3MagicSquaresofOrder5 ..................................... 62 25.4MagicSquaresofOrder6 ..................................... 63 4 Inder J. Taneja https://numbers-magic.com; www.inderjtaneja.wordpress.com 26 and 2026 in Numbers and Magic Squares, Zenodo, December 22, 2025, pp. 1-74, https://doi.org/10.5281/zenodo.17944238 25.5MagicSquaresofOrder7 ..................................... 63 25.6MagicSquaresofOrder8 ..................................... 63 25.7MagicSquaresofOrder9 ..................................... 64 25.8MagicSquaresofOrder10..................................... 64 25.9MagicSquaresofOrder11..................................... 65 25.10MagicSquaresofOrder12..................................... 65 25.11Upside-DownMagicSquares ................................... 66 25.11.1MagicSquaresofOrder4 ................................. 66 25.11.2MagicSquaresofOrder5 ................................. 67 5 Inder J. Taneja https://numbers-magic.com; www.inderjtaneja.wordpress.com 26 and 2026 in Numbers and Magic Squares, Zenodo, December 22, 2025, pp. 1-74, https://doi.org/10.5281/zenodo.17944238 1 Upside-down and Mirror Looking Representations of 26 and 2026 1.1 Representations of 26 The representations given below lead us to sum 26. 1.1.1 First-Type: Upside-down and Mirror Looking 1.1.2 Second-Type: Upside-down and Mirror Looking 1.1.3 Third-Type: Upside-down The above expressions are upside-down and mirror looking, i.e., universal summing to 26. 1.2 Representations of 2026 The representations given below lead us to sum 2026. 6 Inder J. Taneja https://numbers-magic.com; www.inderjtaneja.wordpress.com 26 and 2026 in Numbers and Magic Squares, Zenodo, December 22, 2025, pp. 1-74, https://doi.org/10.5281/zenodo.17944238 1.2.1 First-Type: Upside-down and Mirror Looking 1.2.2 Second-Type: Upside-down and Mirror Looking 1.2.3 Third-Type: Upside-down and Mirror Looking 1.2.4 Forth-Type: Upside-down and Mirror Looking 7 Inder J. Taneja https://numbers-magic.com; www.inderjtaneja.wordpress.com 26 and 2026 in Numbers and Magic Squares, Zenodo, December 22, 2025, pp. 1-74, https://doi.org/10.5281/zenodo.17944238 1.2.5 Fifth-Type: Upside-down 8 Inder J. Taneja https://numbers-magic.com; www.inderjtaneja.wordpress.com 26 and 2026 in Numbers and Magic Squares, Zenodo, December 22, 2025, pp. 1-74, https://doi.org/10.5281/zenodo.17944238 2 2026 in Magic Squares of Order 4 2.1 First-Way Above there are 46 equal sums pandiagonal magic squares of order 4 with magic sum S4×4:=1474. 9 Inder J. Taneja https://numbers-magic.com; www.inderjtaneja.wordpress.com 26 and 2026 in Numbers and Magic Squares, Zenodo, December 22, 2025, pp. 1-74, https://doi.org/10.5281/zenodo.17944238 11. 8+8+8+ (8+8)/8 :=26 88 +8+8+ (88 +88)/8 :=126 888 +8+8+ (888 +888)/8 :=1126 8888 +8+8+ (8888 +8888)/8 :=11126 12. 8+8+8+ (8+8)/8 :=26 88 +88 +88 + (88 +88):=286 888 +888 +888 + (888 +888):=2886 8888 +8888 +8888 + (8888 +8888):=28886 13. 9+9+9−9/9 :=26 99 +99 +9−9/9 :=206 999 +999 +9−9/9 :=2006 9999 +9999 +9−9/9 :=20006 14. 9+9+9−9/9 :=26 99 +99 +99 −9/9 :=296 999 +999 +999 −9/9 :=2996 9999 +9999 +9999 −9/9 :=29996 5.1.2 Pattern in Single Digit for 2026 1. 333 ×(3+3) + 33+3/3 :=2026 3333 ×(3+3)) + 33+3/3 :=20026 33333 ×(3+3)) + 33+3/3 :=200026 333333 ×(3+3)) + 33+3/3 :=2000026 2. (66 ×6+6+ (6+6)/6)×(6−6/6) + 6 :=2026 (666 ×6+6+ (6+6)/6)×(6−6/6) + 6 :=20026 (6666 ×6+6+ (6+6)/6)×(6−6/6) + 6 :=200026 (66666 ×6+6+ (6+6)/6)×(6−6/6) + 6 :=2000026 3. (66 ×6+6+ (6+6)/6)×(6−6/6) + 6 :=2026 (666 ×6+66 + (6+6)/6)×(6−6/6) + 6 :=20326 (6666 ×6+666 + (6+6)/6)×(6−6/6) + 6 :=203326 (66666 ×6+6666 + (6+6)/6)×(6−6/6) + 6 :=2033326 16 Inder J. Taneja https://numbers-magic.com; www.inderjtaneja.wordpress.com 26 and 2026 in Numbers and Magic Squares, Zenodo, December 22, 2025, pp. 1-74, https://doi.org/10.5281/zenodo.17944238 4. 88 ×(8+8+8−8/8) + (8+8)/8 :=2026 888 ×(8+8+8−8/8) + (8+8)/8 :=20426 8888 ×(8+8+8−8/8) + (8+8)/8 :=204426 88888 ×(8+8+8−8/8) + (8+8)/8 :=2044426 6 Single Letter Representations 26 :=(aa +a+a)×(a+a) a×a 2026 :=(aaaa −aaa +aa +a+a)×(a+a) a×a where,aaaaa =a104+a103+a102+a10 +a, aaaa =a103+a102+a10 +a, aaa =a102+a10 +a, aa =a10 +a, etc. a∈ {1, 2, 3, 4, 5, 6, 7, 8, 9}. 6.1 Patterns in Single Letter for 26 1. (aa +a+a)×(a+a)/(a×a):=26 (aaa +a+a)×(a+a)/(a×a):=226 (aaaa +a+a)×(a+a)/(a×a):=2226 (aaaaa +a+a)×(a+a)/(a×a):=22226 2. (aa +a+a)×(a+a)/(a×a):=26 (aa +aaa +aa)×(a+a)/(a×a):=266 (aaaa +aaa +aaa)×(a+a)/(a×a):=2666 (aaaaa +aaaa +aaaa)×(a+a)/(a×a):=26666 17 Inder J. Taneja https://numbers-magic.com; www.inderjtaneja.wordpress.com 26 and 2026 in Numbers and Magic Squares, Zenodo, December 22, 2025, pp. 1-74, https://doi.org/10.5281/zenodo.17944238 6.2 Patterns in Single Letter for 2026 1. (aaaa −aaa +aa +a+a)×(a+a)/(a×a):=2026 (aaaaa −aaaa +aa +a+a)×(a+a)/(a×a):=20026 (aaaaaa −aaaaa +aa +a+a)×(a+a)/(a×a):=200026 (aaaaaaa −aaaaaa +aa +a+a)×(a+a)/(a×a):=2000026 2. (aaaa −aaa +aa +a+a)×(a+a)/(a×a):=2026 (aaaaa −aaaa +aaa +a+a)×(a+a)/(a×a):=200226 (aaaaaa −aaaaa +aaaa +a+a)×(a+a)/(a×a):=20002226 (aaaaaaa −aaaaaa +aaaaa +a+a)×(a+a)/(a×a):=2000022226 3. (aaaa −aaa +aa +a+a)×(a+a)/(a×a):=2026 (aaaaa −aaaa +aaa +aa +aa)×(a+a)/(a×a):=200266 (aaaaaa −aaaaa +aaaa +aaa +aaa)×(a+a)/(a×a):=20002666 (aaaaaaa −aaaaaa +aaaaa +aaaa +aaaa)×(a+a)/(a×a):=2000026666 7 Running Equality Expressions for 26 7.1 Factorial and Square-Root 18 Inder J. Taneja https://numbers-magic.com; www.inderjtaneja.wordpress.com 26 and 2026 in Numbers and Magic Squares, Zenodo, December 22, 2025, pp. 1-74, https://doi.org/10.5281/zenodo.17944238 26 :=−1+23 +4=−56 −7+89 :=1×23 +√4+5= (6+7)×8−√9! :=123 ×4×5+6=78/√9 := (1+2)!+3!! +4×5−6! =78/√9 :=12+34−56 =78/√9 26 := (9−8)7×(6×5−4) = 3! +2×10 :=98 −7−65 =√4+3+21 =4! +3−2+1 =4+32 −10 :=−√9!+8×(7+6) = 5×(4−3) + 21 =54/3 −2+10 7.2 Fibonacci Sequence Values 26 :=1×23 +F(4) = −56 −7+89 :=−F(12) + 34 ×5= (6−7)×(8−F(9)) :=12+34−56 =F(7)−F(8) + F(9) :=12/3 +4+5+6+7=−8+F(9) 26 :=F(9)−8= (F(7) + 65)×(4+3)/21 =−7−F(6)−5+4+32 +10 := (9+F(8)×7)/6 =5×(4−3) + 21 =54/3 ×2−10 :=F(9)−F(8) + F(7) = 65 ×4/(32+1) =F(6) + 5×(4+32)/10 :=98 −7−65 =F(4+3)×2×1 =4+32 −10 19 Inder J. Taneja https://numbers-magic.com; www.inderjtaneja.wordpress.com 26 and 2026 in Numbers and Magic Squares, Zenodo, December 22, 2025, pp. 1-74, https://doi.org/10.5281/zenodo.17944238 7.3 Triangular Numbers 26 :=T(12)/3 = (4+5)×6−7×T(8)/9 :=1×2×3+4×5=6−7+T(8)−9 26 :=9−T(8)−7+6+54 =T(3) + 2×10 :=−9+T(8)−7+6=5×(4−3) + 21 =54/3 −2+10 :=98 −7−65 =T(4×3)/(2+1) =4+32 −10 8 Pythagorean Triples There are very few Pythagorean triples with 26 and 2026 102+242=262 262+1682:=1702 20242+902:=20262 20262+10261682:=10261702 8.1 Pattern in Pythagorean Triples with 26 1. 102+242=262 21702+2642=21862 2217702+26642=2217862 222177702+266642=222177862 20 Inder J. Taneja https://numbers-magic.com; www.inderjtaneja.wordpress.com 26 and 2026 in Numbers and Magic Squares, Zenodo, December 22, 2025, pp. 1-74, https://doi.org/10.5281/zenodo.17944238 2. 262+1682:=1702 2662+176882:=176902 26662+17768882:=17768902 266662+1777688882:=1777688902 3. 102+242:=262 1002+24992:=25012 10002+2499992:=2500012 100002+249999992:=250000012 4. 102+242:=262 1102+30242:=30262 11102+3080242:=3080262 111102+308580242:=308580262 8.2 Pattern in Pythagorean Triples with 2026 1. 20242+902:=20262 2070242+9102:=2070262 207480242+91102:=207480262 20752580242+911102:=20752580262 9 Selfie Representations 21 Inder J. Taneja https://numbers-magic.com; www.inderjtaneja.wordpress.com 26 and 2026 in Numbers and Magic Squares, Zenodo, December 22, 2025, pp. 1-74, https://doi.org/10.5281/zenodo.17944238 26 :=F(Q(F(Q(2)))) −F(6) :=qT(Q(2)) + T(Q(6))) 2026 :=F(2) + Q(Q(0! +2) + Q(6)) :=T(Q(2)) + T(T(02)×T(6)) The functions Q, C, T and Fare respectively, Quadratic, Cubic, Triangular and Fibonacci functions. Still the factorial and square-root are also applied. The above representations we call as selfie representations as they follow the order of the digits 2, 6 and 2, 0, 2, 6. 10 Selfie Fractions for 26 and 2026 10.1 Selfie Fractions for 26 26 39 :=2+6 3+9 26 65 :=2×6 6×5 26 728 :=26 7×28 26 832 :=2+6 8×32 26 1144 :=26 11 ×44 26 1248 :=2+6 12 ×4×8 26 1248 :=2×6 12 ×48 26 1638 :=2+6 1×63 ×8 26 1768 :=2+6 (1+7)×68 26 1768 :=2×6 (7×6×8 26 1872 :=2+6 1×8×72 26 1898 :=2+6 (1+8×9)×8 26 2184 :=2+6 21 ×8×4 26 2392 :=2+6 23×92 26 2496 :=2+6 2×4×96 26 3328 :=2×6 (3+3)×28 26 4264 :=2+6 42+64 26 6318 :=2+6 63×(1+8) 26 11232 :=2+6 1×123×2 26 12636 :=2+6 (1+2)×63×6 26 12636 :=2×6 (1×2+6)×36 26 13312 :=2+6 (13 +3)(1+2) 22 Inder J. Taneja https://numbers-magic.com; www.inderjtaneja.wordpress.com 26 and 2026 in Numbers and Magic Squares, Zenodo, December 22, 2025, pp. 1-74, https://doi.org/10.5281/zenodo.17944238 26 13338 :=2+6 (13 +3)3+8 26 14625 :=2+6 (1+4)×6)2×5 26 16536 :=2+6 16 ×53 ×6 26 16965 :=2×6 1×6×9+65 26 17771 :=2+6 1+77 ×71 10.2 Patterns in Selfie Fractions for 26 1. 26 143 :=2+6 1+43 26 1443 :=2+6 1+443 26 14443 :=2+6 1+4443 26 144443 :=2+6 1+44443 2. 26 286 :=2+6 2+86 26 2886 :=2+6 2+886 26 28886 :=2+6 2+8886 26 288886 :=2+6 2+88886 3. 26 260 :=2×6 2×60 26 2600 :=2×6 2×600 26 26000 :=2×6 2×6000 26 260000 :=2×6 2×60000 4. 26 65 :=2×6 6×5 26 650 :=2×6 6×50 26 6500 :=2×6 6×500 26 65000 :=2×6 6×5000 10.3 Selfie Fractions for 2026 2026 14182 :=2×0×2+6 (1+4)×1×8+2 :=2×(0×2+6) 14+1+82 :=2×026 14 ×1×82 :=2+0×26 1×4×1+8+2 23 Inder J. Taneja https://numbers-magic.com; www.inderjtaneja.wordpress.com 26 and 2026 in Numbers and Magic Squares, Zenodo, December 22, 2025, pp. 1-74, https://doi.org/10.5281/zenodo.17944238 :=2+0+2×6 (1×41 +8)×2 :=2+02 +6 (1+4+1+8)2 :=2+026 (1+4+1+8)2 :=20 +2×6 14 ×1×8×2 2026 15195 :=2×0×2+6 15×1×9×5 :=2×(0×2+6) 15 ×(19+5) :=2×(02 +6 1×5×(19 +5) :=2(0×2+6 1×5×(1+95) :=2+0×2+6 1+ (5+1)×9+5 :=2+0×26 15+1×9+5 :=2+02 +6 1×5×(1+9+5) :=2+026 15 ×(1×9+5) 2026 16208 :=2×(0×2+6) 1×6×2×08 :=2×(02 +6 1×6×20 +8 :=202+6 162×08 :=2+0×2+6 (1×6+2)×08 :=2+0×26 1×6+2+08 :=2+02 ×6 (1+6)×2×08 :=2+026 16 +208 :=20 +2×6 16 ×2×08 2026 17221 :=2×0×2+6 1×72+2×1 :=2×(0×2+6) 17 ×2×(2+1) :=2×(02 +6) 17 ×22+1 :=2+0×2+6 17 ×22×1 :=2+0×26 1+7×2+2×1 :=2+02 +6 17 ×(2+2+1) :=2+026 17 +221 :=20 +26 17 ×2×21 :=20 +26 17 ×(2+21) :=202 +6 (1+7)×221 2026 18234 :=2×0×2+6 18 +2+34 :=(22)6 (1+8)×(23)4 24 Inder J. Taneja https://numbers-magic.com; www.inderjtaneja.wordpress.com 26 and 2026 in Numbers and Magic Squares, Zenodo, December 22, 2025, pp. 1-74, https://doi.org/10.5281/zenodo.17944238 :=2×(0×2+6) (18+2)3×4 :=2×02 ×6 1×8×(23 +4) :=2×026 (1+8)×23+4 :=20×2+6 18 ×23×4 :=202+6 18 ×23+4 :=2+0×2+6 1×8×(2+3+4) :=2+0×26 1+8+2+3+4 :=2+0+2×6 (1+8)×2×(3+4) :=2+02 +6 1+82 +3+4 :=2+026 18 ×2×(3+4) :=20 +2×6 1×8×(2+34) :=202 +6 1×8×234 1013 2026 :=1+0×13 2+0×26 :=1×01 ×3 2×0×2+6 :=1×01 +3 2+0×2+6 :=1+01 +3 2+02 +6 :=(1+01)×3 2×(0×2+6) :=(1+01)3 2×(02 +6) :=1+013 2+026 :=10 +13 20 +26 :=(10 +1)×3 2+026 :=101 +3 202 +6 2026 3039 :=2+0×26 3+0×39 :=2+02 +6 3+03 +9 :=2×(0×2+6) 3×03 +9 :=2×02 ×6 3×(03 +9) :=2+026 3+039 :=2×0×2+6 3×0×3+9 :=20 +26 30 +39 :=2+0×2+6 3+0×39) :=2+026 30 ×3+9 :=202 +6 303 +9 :=20 ×2×6 30 ×(3+9) 2026 11143 :=2+0×26 (1+11)×4+3):=2+02 +6 1+11 +43 25 Inder J. Taneja https://numbers-magic.com; www.inderjtaneja.wordpress.com 26 and 2026 in Numbers and Magic Squares, Zenodo, December 22, 2025, pp. 1-74, https://doi.org/10.5281/zenodo.17944238 25. 2026 18234 :=2×(0×2+6) (18+2)3×4 2026 182340 :=2×(0×2+6) (18+2)3×40 2026 1823400 :=2×(0×2+6) (18+2)3×400 2026 18234000 :=2×(0×2+6) (18+2)3×4000 26. 2026 18234 :=202 +6 1×8×234 2026 182340 :=202 +6 1×8×2340 2026 1823400 :=202 +6 1×8×23400 2026 18234000 :=202 +6 1×8×234000 27. 2026 18234 :=20×2+6 (18 ×23×4 2026 182340 :=20×2+6 (18 ×23×40 2026 1823400 :=20×2+6 (18 ×23×400 2026 18234000 :=20×2+6 (18 ×23×4000 28. 2026 8104 :=2+0×2+6 8×04 2026 81040 :=2+0×2+6 8×040 2026 810400 :=2+0×2+6 8×0400 2026 8104000 :=2+0×2+6 8×04000 29. 2026 8104 :=202 +6 8×104 2026 81040 :=202 +6 8×1040 2026 810400 :=202 +6 8×10400 2026 8104000 :=202 +6 8×104000 30. 2026 9117 :=2+0+2×6 9×1×1×7 2026 91170 :=2+0+2×6 9×1×1×70 2026 911700 :=2+0+2×6 9×1×1×700 2026 9117000 :=2+0+2×6 9×1×1×7000 32 Inder J. Taneja https://numbers-magic.com; www.inderjtaneja.wordpress.com 26 and 2026 in Numbers and Magic Squares, Zenodo, December 22, 2025, pp. 1-74, https://doi.org/10.5281/zenodo.17944238 11 Equivalent Fractions 11.1 Equivalent Fractions for 26 26 14573 :=62 34751 26 15743 :=62 37541 26 145730 :=62 347510 26 157430 :=62 375410 26 137854 :=78 413562 26 138745 :=78 416235 26 143875 :=78 431625 26 145873 :=62 347851 26 153784 :=78 461352 26 157384 :=52 314768 26 157438 :=52 314876 26 158374 :=52 316748 26 158437 :=52 316874 26 158734 :=52 317468 26 173584 :=52 347168 26 174358 :=52 348716 26 175438 :=78 526314 26 183574 :=52 367148 26 184357 :=52 368714 26 185734 :=52 371468 26 185743 :=52 371486 26 315874 :=52 631748 26 318574 :=52 637148 26 341587 :=52 683174 26 341857 :=52 683714 26 354718 :=64 873152 26 357184 :=52 714368 26 357418 :=52 714836 26 358174 :=52 716348 26 358417 :=52 716834 26 371584 :=52 743168 26 374158 :=52 748316 26 381574 :=52 763148 26 384157 :=52 768314 26 415738 :=52 831476 26 415837 :=52 831674 26 415873 :=52 831746 26 417358 :=52 834716 26 418357 :=52 836714 26 418573 :=52 837146 26 431587 :=52 863174 26 431857 :=52 863714 26 435718 :=52 871436 26 435817 :=52 871634 26 437158 :=52 874316 26 438157 :=52 876314 33 Inder J. Taneja https://numbers-magic.com; www.inderjtaneja.wordpress.com 26 and 2026 in Numbers and Magic Squares, Zenodo, December 22, 2025, pp. 1-74, https://doi.org/10.5281/zenodo.17944238 26 153478 :=46 271538 =54 318762 26 158743 :=52 317486 =62 378541 26 174538 :=57 382641 =78 523614 26 15849730 :=36 21945780 =54 32918670 =72 43891560 26 19473805 :=52 38947610 =84 62915370 =98 73401265 26 15498730 :=27 16094835 =36 21459780 =47 28016935 =54 32189670 12 Narcissistic Type Representations 12.1 Narcissistic Type Representations for 26 26 :=24+62 20+60=−23+63 21+61 12.2 Narcissistic Type Representations for 2026 2026 :=−24+01+211 −61 −20−00+21+60 13 Semi-Selfie Representations 13.1 Powers of 26 34 Inder J. Taneja https://numbers-magic.com; www.inderjtaneja.wordpress.com 26 and 2026 in Numbers and Magic Squares, Zenodo, December 22, 2025, pp. 1-74, https://doi.org/10.5281/zenodo.17944238 ▶263:=17576 = (1+7+5+7+6)3 ▶265:=11881376 = (11 +8+8+1−3+7−6)5 = (11 +8−8−1+3+7+6)5 ▶266:=308915776 = (3+08 −9−1+5+7+7+6)6 = (3+08 +91 −5−77 +6)6 ▶267:=8031810176 = (−8+031 −8−1−01 +7+6)7 = (80 −3−18 −10 −17 −6)7 13.2 Power as 26 ▶226 :=67108864 = (6+7−1+08 −8−6−4)26 = (67 −1+08 −8−64)26 14 Power Representations 14.1 Powers of 2 2026 :=210 +29+28+27+26+25+24−23+21 :=210 +29+28+27+26+25+24−23+22−21 14.2 Power 2 26 :=12+52 2026 :=12+452 :=12+272+362 :=152+242+352 :=12+202+282+292 35 Inder J. Taneja https://numbers-magic.com; www.inderjtaneja.wordpress.com 26 and 2026 in Numbers and Magic Squares, Zenodo, December 22, 2025, pp. 1-74, https://doi.org/10.5281/zenodo.17944238 14.3 10000+2026: Power 2 10000 +2026 :=12+122+1092 :=12+192+1082 :=12+242+1072 :=12+452+1002 :=12+532+962 :=12+752+802 :=32+642+892 :=32+762+792 :=42+472+992 :=42+512+972 :=82+92+1092 :=92+592+922 :=112+332+1042 :=112+362+1032 :=122+412+1012 :=152+402+1012 :=172+442+992 :=192+642+872 :=202+512+952 :=232+362+1012 :=242+292+1032 :=242+652+852 :=252+402+992 :=252+752+762 :=292+682+812 :=312+432+962 :=312+512+922 :=322+692+792 :=362+532+892 :=362+672+792 :=372+642+812 :=412+512+882 :=442+692+732 :=452+652+762 :=482+592+792 :=512+552+802 :=512+642+732 14.4 Patterns with Powers 3 and 4 2026 0 :=93+143+163+183+193 2026 1 :=13+93+143+163+183+193 2026 2 :=53+73+93+103+133+163+173+193 2026 3 :=13+53+73+93+103+133+163+173+193 2026 4 :=43+63+103+133+163+183+193 2026 5 :=13+43+63+103+133+163+183+193 2026 6 :=53+113+143+153+183+193 2026 7 :=63+83+93+143+153+183+193 2026 8 :=23+93+143+163+183+193 2026 9 :=53+73+133+173+183+193 12026 :=43+123+153+193 22026 :=33+103+123+133+143+153+163+193 32026 :=13+43+63+93+103+133+143+153+163+173+183+193 36 Inder J. Taneja https://numbers-magic.com; www.inderjtaneja.wordpress.com 26 and 2026 in Numbers and Magic Squares, Zenodo, December 22, 2025, pp. 1-74, https://doi.org/10.5281/zenodo.17944238 12026 0 :=14+44+74+134+144+154 12026 1 :=34+64+74+94+104+124+134+154 12026 2 :=14+34+64+74+94+104+124+134+154 15 Square-Power Patterns 15.1 Square-Power Patterns for 26 1. 262:=676 2762:=76176 27762:=7706176 277762:=771506176 2. 262:=676 3262:=106276 33262:=11062276 333262:=1110622276 15.2 Square-Power Patterns for 2026 1. 20262:=4104676 200262:=401040676 2000262:=40010400676 20000262:=4000104000676 2. 20262+62022:=4104676 +38464804 200262+620022:=401040676 +3844248004 2000262+6200022:=40010400676 +384402480004 20000262+62000022:=4000104000676 +38440024800004 37 Inder J. Taneja https://numbers-magic.com; www.inderjtaneja.wordpress.com 26 and 2026 in Numbers and Magic Squares, Zenodo, December 22, 2025, pp. 1-74, https://doi.org/10.5281/zenodo.17944238 16 Power-Plus-Minus Equalities 16.1 Power-Plus-Minus Equalities for 26 26 :=14−21+33=14 −21 +33 :=15−250+261=15 −250 +261 :=16−122+132=16 −122 +132 :=12+12−50+52=12 +12 −50 +52 :=10+14−23+25=10 +14 −23 +25 :=11+13−23+25=11 +13 −23 +25 :=11+25+32−42=11 +25 +32 −42 :=12+25+70−81=12 +25 +70 −81 :=12+46+52−84=12 +46 +52 −84 :=13+33+41−61=13 +33 +41 −61 :=13+42+42−71=13 +42 +42 −71 :=14+20+52−60=14 +20 +52 −60 :=14+40+52−80=14 +40 +52 −80 :=14+50+52−90=14 +50 +52 −90 :=27+1030−1031=27 +1030 −1031 :=14+45+70−103=14 +45 +70 −103 :=24+51+61−110=24 +51 +61 −110 :=24+53+61−112=24 +53 +61 −112 :=48+52+90−164=48 +52 +90 −164 :=13+33+81−101=13 +33 +81 −101 :=11+45+93−123=11 +45 +93 −123 :=14+21+241−250=14 +21 +241 −250 :=14+51+211−250=14 +51 +211 −250 :=16−21−250+281=16 −21 −250 +281 :=25+32+130−161=25 +32 +130 −161 :=52+58+170−254=52 +58 +170 −254 :=10+15−250+251=10 +15 −250 +251 :=10+26+192−202=10 +26 +192 −202 :=10−15−240+271=10 −15 −240 +271 :=11+14−250+251=11 +14 −250 +251 :=11+24+101−110=11 +24 +101 −110 :=11+36+251−272=11 +36 +251 −272 :=12+13−250+251=12 +13 −250 +251 :=12+23+181−190=12 +23 +181 −190 :=12+34+132−152=12 +34 +132 −152 :=12−17−240+271=12 −17 −240 +271 :=13+22+221−230=13 +22 +221 −230 :=13+32+171−190=13 +32 +171 −190 :=13+33+281−301=13 +33 +281 −301 :=13+42+101−130=13 +42 +101 −130 :=14+131+131−250=14 +131 +131 −250 :=36+101+161−272=36 +101 +161 −272 :=32+38−43+64−65=32 +38 −43 +64 −65 :=42+49−86−90+111=42 +49 −86 −90 +111 16.2 Power-Plus-Minus Equalities for 2026 2026 :=64+272+1690=64 +272 +1690 :=13+442+690+881=13 +442 +690 +881 :=23+442+750+811=23 +442 +750 +811 :=73+402+730+821=73 +402 +730 +821 :=83+382+691+870=83 +382 +691 +870 :=93+352+711+870=93 +352 +711 +870 :=192+392+551+891=192 +392 +551 +891 :=192+392+561+881=192 +392 +561 +881 :=192+392+571+871=192 +392 +571 +871 :=192+392+581+861=192 +392 +581 +861 :=192+392+591+851=192 +392 +591 +851 :=192+392+601+841=192 +392 +601 +841 38 Inder J. Taneja https://numbers-magic.com; www.inderjtaneja.wordpress.com 26 and 2026 in Numbers and Magic Squares, Zenodo, December 22, 2025, pp. 1-74, https://doi.org/10.5281/zenodo.17944238 :=192+392+611+831=192 +392 +611 +831 :=192+392+621+821=192 +392 +621 +821 :=192+392+631+811=192 +392 +631 +811 :=192+392+641+801=192 +392 +641 +801 :=192+392+651+791=192 +392 +651 +791 :=192+392+661+781=192 +392 +661 +781 :=192+392+671+771=192 +392 +671 +771 :=192+392+681+761=192 +392 +681 +761 :=192+392+691+751=192 +392 +691 +751 :=192+392+701+741=192 +392 +701 +741 :=192+392+711+731=192 +392 +711 +731 :=192+392+721+721=192 +392 +721 +721 :=272+342+521+891=272 +342 +521 +891 :=272+342+531+881=272 +342 +531 +881 :=272+342+541+871=272 +342 +541 +871 :=272+342+551+861=272 +342 +551 +861 :=272+342+561+851=272 +342 +561 +851 :=272+342+571+841=272 +342 +571 +841 :=272+342+581+831=272 +342 +581 +831 :=272+342+591+821=272 +342 +591 +821 :=272+342+601+811=272 +342 +601 +811 :=272+342+611+801=272 +342 +611 +801 :=272+342+621+791=272 +342 +621 +791 :=272+342+631+781=272 +342 +631 +781 :=272+342+641+771=272 +342 +641 +771 :=272+342+651+761=272 +342 +651 +761 :=272+342+661+751=272 +342 +661 +751 :=272+342+671+741=272 +342 +671 +741 :=272+342+681+731=272 +342 +681 +731 :=272+342+691+721=272 +342 +691 +721 :=272+342+701+711=272 +342 +701 +711 17 Factorial-Power Equalities 17.1 Factorial-Power Equalities for 26 26 :=3! ×4! +0! +1! −5! = (33+44×0)×15−50 :=3! ×4! +0! +1! −5! = (33+44×05)×11−50 :=3! ×4! +0! +1! −5! =33−40+04×11×55 :=3! ×4! +0! +1! −5! =33−40+5×04×15 :=3! ×4! +0! +1! −5! =33−40+ (0×14)×55 :=3! ×4! +0! +1! −5! =33−40+ (0×15)×54 :=3! ×4! +0! +1! −5! =33−40+5×05×14 :=3! ×4! +0! +1! −5! =33−40+05×11×54 :=3! ×4! +0! +1! −5! = (33+4×04)×15−50 :=3! ×4! +0! +1! −5! = (33+4×05)×14−50 :=3! ×4! +0! +1! −5! = (33+45×04)×11−50 :=3! ×4! +0! +1! −5! = (33+45×0)×14−50 :=3! ×4! ×0! +2! −5! =33+44×02×25−50 :=3! ×4! ×0! +2! −5! = (33+44)×05+20+52 :=3! ×4! ×0! +2! −5! =33+44×05×22−50 :=3! ×4! ×0! +2! −5! =33−40+04×22×55 :=3! ×4! ×0! +2! −5! =33−40+04×25×52 :=3! ×4! ×0! +2! −5! =33−40+02×24×55 :=3! ×4! ×0! +2! −5! =33−40+02×25×54 :=3! ×4! ×0! +2! −5! =33−40+05×24×52 :=3! ×4! ×0! +2! −5! =33−40+05×22×54 :=3! ×4! ×0! +2! −5! =33+42×04×25−50 :=3! ×4! ×0! +2! −5! =33+42+05−24−50 :=3! ×4! ×0! +2! −5! = (33+45)×04+20+52 :=3! ×4! ×0! +2! −5! =33+45×04×22−50 :=3! ×4! ×0! +2! −5! =33+45×02×24−50 :=3! ×4! ×0! +2! −5! = (34+43)×05+20+52 :=3! ×4! ×0! +2! −5! = (34+45)×03+20+52 :=3! ×4! ×0! +2! −5! =30+43×04×25+52 :=3! ×4! ×0! +2! −5! =30+43×05×24+52 39 Inder J. Taneja https://numbers-magic.com; www.inderjtaneja.wordpress.com 26 and 2026 in Numbers and Magic Squares, Zenodo, December 22, 2025, pp. 1-74, https://doi.org/10.5281/zenodo.17944238 :=3! ×4! ×0! +2! −5! =30+44×03×25+52 :=3! ×4! ×0! +2! −5! =30+44×05×23+52 :=3! ×4! ×0! +2! −5! =30+45×03×24+52 :=3! ×4! ×0! +2! −5! =30+45×04×23+52 :=3! ×4! ×0! +2! −5! =32+43×05+24+50 :=3! ×4! ×0! +2! −5! =32+45×03+24+50 :=3! ×4! ×0! +2! −5! = (35+43)×04+20+52 :=3! ×4! ×0! +2! −5! = (35+44)×03+20+52 :=3! ×4! +0! +1! −5! = (33+44×05)×50−11 :=3! ×4! +0! +1! −5! =33+5×44×05−10 :=3! ×4! +0! +1! −5! = (33+44×0)×50−15 :=3! ×4! +0! +1! −5! =33+ (44×0)×55−10 :=3! ×4! +0! +1! −5! =33×40+04×55−11 :=3! ×4! +0! +1! −5! =33×40+5×04−15 :=3! ×4! +0! +1! −5! =33×40+05×54−11 :=3! ×4! +0! +1! −5! =33×40+5×05−14 :=3! ×4! +0! +1! −5! =33×40+0×54−15 :=3! ×4! +0! +1! −5! =33×40+0×55−14 :=3! ×4! +0! +1! −5! = (33+45×04)×50−11 :=3! ×4! +0! +1! −5! =33+5×45×04−10 :=3! ×4! +0! +1! −5! =33+ (45×0)×54−10 :=3! ×4! +0! +1! −5! = (33+45×0)×50−14 :=3! ×4! +0! +1! −5! = (33+4×04)×50−15 :=3! ×4! +0! +1! −5! =33+4×04×55−10 :=3! ×4! +0! +1! −5! =33+4×05×54−10 :=3! ×4! +0! +1! −5! = (33+4×05)×50−14 :=3! ×4! ×0! +2! −5! = (33+44)×05+20+52 :=3! ×4! ×0! +2! −5! =33+44×02×55−20 :=3! ×4! ×0! +2! −5! =33−40+04×22×55 :=3! ×4! ×0! +2! −5! =33−40+04×25×52 :=3! ×4! ×0! +2! −5! =33−40+05×22×54 :=3! ×4! ×0! +2! −5! =33−40+05×24×52 :=3! ×4! ×0! +2! −5! =33−40+02×25×54 :=3! ×4! ×0! +2! −5! =33−40+02×24×55 :=3! ×4! ×0! +2! −5! = (33+45)×04+20+52 :=3! ×4! ×0! +2! −5! =33+45×02×54−20 :=3! ×4! ×0! +2! −5! =33+42×04×55−20 :=3! ×4! ×0! +2! −5! =33+42×05×54−20 :=3! ×4! ×0! +2! −5! =33+42+05−24−50 :=3! ×4! ×0! +2! −5! = (34+43)×05+20+52 :=3! ×4! ×0! +2! −5! = (34+45)×03+20+52 :=3! ×4! ×0! +2! −5! = (35+43)×04+20+52 :=3! ×4! ×0! +2! −5! = (35+44)×03+20+52 18 Fibonacci-Triangular Equalities 18.1 Factorial-Fibonacci-Trianguar Equalities for 26 26 := (F(1) + F(2)) ×(−F(3) + F(4)) ×F(7) = (T(1)−T(2)) ×T(3) + T(4) + T(7) := (F(1) + F(2)) ×(F(3)×F(5) + F(4)) = (T(1) + T(2)) ×(−T(3) + T(5)) −T(4) := (−F(1)×F(2)−F(3) + F(5)) ×F(7) = (T(1) + T(2)−T(3)) ×(T(5)−T(7)) :=F(1) + F(2) + F(4)×(F(7)−F(5)) = T(1)×T(2) + T(4) + T(7)−T(5) := (F(1) + F(2)) ×F(5) + F(4) + F(7) = T(1)×T(2) + T(4) + T(7)−T(5) := (F(1) + F(2)) ×(−F(5)−F(4) + F(8)) = (T(1)−T(2)) ×(T(5)−T(4)) + T(8) := ((F(1) + F(2)) ×F(5)−F(6)) ×F(7) = T(1) + T(2) + T(5)−T(6) + T(7) := (F(1) + F(2)) ×F(5) + F(4) + F(7) = T(1)×T(2) + T(4) + T(7)−T(5) :=F(1)×F(2)×F(5) + F(7) + F(6) = T(1) + T(2) + T(5)−T(6) + T(7) := (F(1) + F(2)) ×(F(5)−F(7) + F(8)) = T(1)×T(2) + T(5)−T(7) + T(8) 40 Inder J. Taneja https://numbers-magic.com; www.inderjtaneja.wordpress.com 26 and 2026 in Numbers and Magic Squares, Zenodo, December 22, 2025, pp. 1-74, https://doi.org/10.5281/zenodo.17944238 := (F(1) + F(2)) ×(F(5)−F(7) + F(8)) = T(1)×T(2) + T(5)−T(7) + T(8) :=−F(1)−(F(2)−F(6)) ×F(3) + F(7) = (T(1)−T(2)) ×(T(6)−T(3)−T(7)) :=F(1) + F(2) + F(6) + F(4) + F(7) = T(1) + T(2)×T(6)−T(4)−T(7) :=F(1)×F(2)×F(6) + F(5) + F(7) = T(1) + T(2) + T(5)−T(6) + T(7) :=F(1) + F(2) + F(6) + F(4) + F(7) = T(1) + T(2)×T(6)−T(4)−T(7) :=F(1)×F(2)×F(6) + F(5) + F(7) = T(1) + T(2) + T(5)−T(6) + T(7) :=−F(1)−F(2) + F(7) + F(4)×F(5) = T(1)×T(2) + T(4) + T(7)−T(5) :=−F(1)−F(2) + F(7) + F(4)×F(5) = T(1)×T(2) + T(4) + T(7)−T(5) :=−F(1)×F(2)−F(7) + F(5)×F(6) = T(1) + T(2) + T(5)−T(6) + T(7) := (F(1) + F(2)) ×(F(5)−F(7) + F(8)) = T(1)×T(2) + T(5)−T(7) + T(8) :=−F(1)×F(2)×F(7) + F(5) + F(9) = (−T(1) + T(2)) ×T(7) + T(5)−T(9) :=−F(1)×F(2)−F(7) + F(5)×F(6) = T(1) + T(2) + T(5)−T(6) + T(7) :=F(1)×F(2)×F(7)−F(6) + F(8) = −T(1)×T(2)−T(7) + T(6) + T(8) :=F(1) + F(2)−(F(7)−F(8)) ×F(4) = (T(1)−T(2)) ×(T(7)−T(8)) + T(4) := (F(1) + F(2)) ×(−F(7) + F(8) + F(5)) = T(1)×T(2) + T(5)−T(7) + T(8) :=F(1)×F(2)×F(7)−F(6) + F(8) = −T(1)×T(2) + T(8) + T(6)−T(7) :=−F(1)×F(2)×F(7) + F(9) + F(5) = (−T(1) + T(2)) ×T(7) + T(5)−T(9) :=F(1)×F(2)×F(8) + F(3) + F(4) = −T(1) + T(2)−T(8) + T(3)×T(4) := (F(1) + F(2)) ×F(8)−F(3)×F(6) = −T(1) + T(2)×(T(8)−T(3)−T(6)) :=F(1)×F(2)×F(8) + F(3) + F(4) = −T(1) + T(2)−T(8) + T(3)×T(4) :=F(1) + F(2) + F(8)−F(5) + F(6) = −T(1)−T(2) + T(8) + T(5)−T(6) := (F(1) + F(2)) ×(F(5)−F(7) + F(8)) = T(1)×T(2) + T(5)−T(7) + T(8) := (F(1) + F(2)) ×F(8)−F(3)×F(6) = −T(1) + T(2)×(T(8)−T(3)−T(6)) :=F(1) + F(2) + F(8)−F(5) + F(6) = −T(1)−T(2) + T(8) + T(5)−T(6) :=F(1)×F(2)×F(8)−F(6) + F(7) = −T(1)×T(2) + T(8) + T(6)−T(7) := (F(1) + F(2)) ×F(8)−F(7)−F(4) = (−T(1) + T(2)) ×(T(8)−T(7)) + T(4) := (F(1) + F(2)) ×(F(5)−F(7) + F(8)) = T(1)×T(2) + T(5)−T(7) + T(8) :=F(1)×F(2)×F(8)−F(6) + F(7) = −T(1)×T(2) + T(8) + T(6)−T(7) :=−F(1)−F(2) + F(9)−F(3)×F(4) = −T(1)×T(2) + T(9)−T(3)−T(4) :=F(1) + F(2) + F(9)−F(3)×F(5) = −T(1) + T(2) + T(9)−T(3)−T(5) :=F(1) + F(2) + F(9)−F(3)−F(6) = −T(1)−T(2) + T(9) + T(3)−T(6) :=F(1) + (F(3)×F(2) + F(4)) ×F(5) = (T(1) + T(3)) ×T(2)−T(4) + T(5) :=F(1) + F(3)−F(2) + F(4)×F(6) = −T(1)−T(3) + T(2)×(−T(4) + T(6)) := (−F(1)×F(3) + F(2) + F(4)) ×F(7) = −T(1) + T(3) + T(2)−T(4) + T(7) :=−F(1)×F(3)×(F(2) + F(4)) + F(9) = −T(1)×T(3)−T(2)−T(4) + T(9) := (F(1) + F(3)−F(2)) ×(F(5) + F(6)) = −T(1)−T(3)−T(2) + T(5) + T(6) 41 Inder J. Taneja https://numbers-magic.com; www.inderjtaneja.wordpress.com 26 and 2026 in Numbers and Magic Squares, Zenodo, December 22, 2025, pp. 1-74, https://doi.org/10.5281/zenodo.17944238 20.2 Palindromic Prime Patterns for 2026 92026 96202 9 99 92026 96202 999 99999 92026 96202 999999 9922299999 92026 96202 99999922299 992229922299999 92026 96202 9999992229922299 9069992229922299999 92026 96202 99999922299222999609 969699069992229922299999 92026 96202 9999992229922299960996969 99022969699069992229922299999 92026 96202 999999222992229996099696922099 96299022969699069992229922299999 92026 96202 999999222992229996099696922099269 96996299022969699069992229922299999 92026 96202 999999222992229996099696922099269969 9292696996299022969699069992229922299999 92026 96202 99999922299222999609969692209926996962929 960069292696996299022969699069992229922299999 92026 96202 9999992229922299960996969220992699696292960069 ... ... ... ... ... ... ... ... 72026202 7 722 72026202 7227 7006722 72026202 72276007 7077006722 72026202 72276007707 77777077006722 72026202 722760077077777 76777777077006722 72026202 722760077077777767 76276777777077006722 72026202 722760077077777767267 7622276276777777077006722 72026202 72276007707777776726722267 7027622276276777777077006722 72026202 72276007707777776726722267207 726267027622276276777777077006722 72026202 7227600770777777672672226720762627 72726267027622276276777777077006722 72026202 722760077077777767267222672076262727 722272726267027622276276777777077006722 72026202 7227600770777777672672226720762627272227 767722272726267027622276276777777077006722 72026202 7227600770777777672672226720762627272227767 7266767722272726267027622276276777777077006722 72026202 72276007707777776726722267207626272722277676627 ... ... ... ... ... ... ... ... 21 Fixed Digits Repetitions Primes Patterns 21.1 Length 7 32026 9 1776 3 2026 9 1776 1776 3 2026 9 1776 1776 1776 3 2026 9 1776 1776 1776 1776 3 2026 9 1776 1776 1776 1776 1776 3 2026 9 1776 1776 1776 1776 1776 1776 3 2026 9 2026 0813 2026 78 0813 48 Inder J. Taneja https://numbers-magic.com; www.inderjtaneja.wordpress.com 26 and 2026 in Numbers and Magic Squares, Zenodo, December 22, 2025, pp. 1-74, https://doi.org/10.5281/zenodo.17944238 2026 78 78 0813 2026 78 78 78 0813 2026 78 78 78 78 0813 2026 78 78 78 78 78 0813 2026 78 78 78 78 78 78 0813 2026 2779 2026 2 39 779 2026 2 39 39 779 2026 2 39 39 39 779 2026 2 39 39 39 39 779 2026 2 39 39 39 39 39 779 2026 2 39 39 39 39 39 39 779 4 3 2026 83 4 48 3 2026 83 4 48 48 3 2026 83 4 48 48 48 3 2026 83 4 48 48 48 48 3 2026 83 4 48 48 48 48 48 3 2026 83 4 48 48 48 48 48 48 3 2026 83 87 2026 57 87 51 2026 57 87 51 51 2026 57 87 51 51 51 2026 57 87 51 51 51 51 2026 57 87 51 51 51 51 51 2026 57 87 51 51 51 51 51 51 2026 57 2026 is not a prime number but the numbers 32026 9,2026 0813,2026 2779,4 3 2026 83 and 87 2026 57, are prime numbers. 21.2 Length 8 2026 3921 2026 392 291 1 2026 392 291 291 1 2026 392 291 291 291 1 2026 392 291 291 291 291 1 2026 392 291 291 291 291 291 1 2026 392 291 291 291 291 291 291 1 2026 392 291 291 291 291 291 291 291 1 92026 261 9573 2026 261 9573 573 2026 261 9573 573 573 2026 261 9573 573 573 573 2026 261 9573 573 573 573 573 2026 261 9573 573 573 573 573 573 2026 261 9573 573 573 573 573 573 573 2026 261 2026 is not a prime number but the numbers 2026 3921 and 92026 261 are prime numbers. 22 Pattern in Multiplication and Division with 26 22.1 Multiplication 037.037.037 ×26 =962 962 962 49 Inder J. Taneja https://numbers-magic.com; www.inderjtaneja.wordpress.com 26 and 2026 in Numbers and Magic Squares, Zenodo, December 22, 2025, pp. 1-74, https://doi.org/10.5281/zenodo.17944238 017.017.017 ×26 :=442 442 442 •Multiplication with Other Numbers 037.037.037 ×01 =037 037 037. 037.037.037 ×10 =370 370 370 037.037.037 ×19 =703 703 703 037.037.037 ×02 =074 074 074 037.037.037 ×11 =407 407 407 037.037.037 ×20 =740 740 740 037.037.037 ×04 =148 148 148 037.037.037 ×13 =481 481 481 037.037.037 ×22 =814 814 814 037.037.037 ×05 =185 185 185 037.037.037 ×14 =518 518 518 037.037.037 ×23 =851 851 851 037.037.037 ×07 =259 259 259 037.037.037 ×16 =592 592 592 037.037.037 ×25 =925 925 925 037.037.037 ×08 =296 296 296 037.037.037 ×17 =629 629 629 037.037.037 ×26 =962 962 962 22.2 Division: Recurring numbers 1 26 =0.038461 538461 538461 538461 538461 538461 . . . =0.038461 538461 •Examples of Other Recurring Numbers 22 7=3.142857 142857 142857 142857 142857 142857 . . . =3. 142857 1 27 =0.037 037 037 037 037 037 037 037 037 037 037 . . . =0. 037 1 81 =0.012345679 012345679 012345679 012345679 . . . =0. 012345679 50 Inder J. Taneja https://numbers-magic.com; www.inderjtaneja.wordpress.com 26 and 2026 in Numbers and Magic Squares, Zenodo, December 22, 2025, pp. 1-74, https://doi.org/10.5281/zenodo.17944238 23 Palindromic-Type Patterns and Expressions 23.1 Palindromic-Type Patterns for 25 1. 968 :=11 ×62 +26 ×11 =682 +286 9768 :=111 ×62 +26 ×111 =6882 +2886 97768 :=1111 ×62 +26 ×1111 =68882 +28886 977768 :=11111 ×62 +26 ×11111 =688882 +288886 2. 8888 :=101 ×62 +26 ×101 =6262 +2626 88088 :=1001 ×62 +26 ×1001 =62062 +26026 880088 :=10001 ×62 +26 ×10001 =620062 +260026 8800088 :=100001 ×62 +26 ×100001 =6200062 +2600026 3. 968 :=11 ×62 +26 ×11 =682 +286 8888 :=11 ×602 +206 ×11 =6622 +2266 88088 :=11 ×6002 +2006 ×11 =66022 +22066 880088 :=11 ×60002 +20006 ×11 =660022 +220066 4. 8888 :=101 ×62 +26 ×101 =6262 +2626 81608 :=101 ×602 +206 ×101 =60802 +20806 808808 :=101 ×6002 +2006 ×101 =606202 +202606 8080808 :=101 ×60002 +20006 ×101 =6060202 +2020606 23.2 Palindromic-Type Patterns for 2026 51 Inder J. Taneja https://numbers-magic.com; www.inderjtaneja.wordpress.com 26 and 2026 in Numbers and Magic Squares, Zenodo, December 22, 2025, pp. 1-74, https://doi.org/10.5281/zenodo.17944238 1. 90508 :=11 ×6202 +2026 ×11 =68222 +22286 913308 :=111 ×6202 +2026 ×111 =688422 +224886 9141308 :=1111 ×6202 +2026 ×1111 =6890422 +2250886 91421308 :=11111 ×6202 +2026 ×11111 =68910422 +22510886 2. 831028 :=101 ×6202 +2026 ×101 =626402 +204626 8236228 :=1001 ×6202 +2026 ×100 =6208202 +2028026 82288228 :=10001 ×6202 +2026 ×10001 =62026202 +20262026 822808228 :=100001 ×6202 +2026 ×100001 =620206202 +202602026 3. 90508 :=11 ×6202 +2026 ×11 =68222 +22286 902308 :=11 ×62002 +20026 ×11 =682022 +220286 9020308 :=11 ×620002 +200026 ×11 =6820022 +2200286 90200308 :=11 ×6200002 +2000026 ×11 =68200022 +22000286 4. 831028 :=101 ×6202 +2026 ×101 =626402 +204626 8284828 :=101 ×62002 +20026 ×101 =6262202 +2022626 82822828 :=101 ×620002 +200026 ×101 =62620202 +20202626 828202828 :=101 ×6200002 +2000026 ×101 =626200202 +202002626 23.3 Palindromic-Type Expressions for 26 1. 7106 :=026 ×11 +11 ×62 0=0286 +6820 8217 :=126 ×11 +11 ×62 1=1386 +6831 9328 :=226 ×11 +11 ×62 2=2486 +6842 10439 :=326 ×11 +11 ×62 3=3586 +6853 52 Inder J. Taneja https://numbers-magic.com; www.inderjtaneja.wordpress.com 26 and 2026 in Numbers and Magic Squares, Zenodo, December 22, 2025, pp. 1-74, https://doi.org/10.5281/zenodo.17944238 11550 :=426 ×11 +11 ×62 4=4686 +6864 12661 :=626 ×11 +11 ×62 5=5786 +6875 13772 :=626 ×11 +11 ×62 6=6886 +6886 14883 :=726 ×11 +11 ×62 7=7986 +6897 15994 :=826 ×11 +11 ×62 8=9086 +6908 17105 :=926 ×11 +11 ×62 9=10186 +6919 2. 55045 :=025 ×101 +101 ×52 0=02525 +52520 65246 :=125 ×101 +101 ×52 1=12625 +52621 75447 :=225 ×101 +101 ×52 2=22725 +52722 85648 :=325 ×101 +101 ×52 3=32825 +52823 95849 :=425 ×101 +101 ×52 4=42925 +52924 106050 :=525 ×101 +101 ×52 5=53025 +53025 116251 :=625 ×101 +101 ×52 6=63125 +53126 126452 :=725 ×101 +101 ×52 7=73225 +53227 136653 :=825 ×101 +101 ×52 8=83325 +53328 146854 :=925 ×101 +101 ×52 9=93425 +53429 We observe that not all the expressions symmetric as expected. 23.4 Palindromic-Type Expressions for 2025 1. 594495 :=02025 ×11 +11 ×5202 0=022275 +572220 704506 :=12025 ×11 +11 ×5202 1=132275 +572231 814517 :=22025 ×11 +11 ×5202 2=572242 +242275 924528 :=32025 ×11 +11 ×5202 3=572253 +352275 1034539 :=42025 ×11 +11 ×5202 4=572264 +462275 1144550 :=52025 ×11 +11 ×5202 5=572275 +572275 1254561 :=62025 ×11 +11 ×5202 6=572286 +682275 1364572 :=72025 ×11 +11 ×5202 7=572297 +792275 1474583 :=82025 ×11 +11 ×5202 8=572308 +902275 1584594 :=92025 ×11 +11 ×5202 9=572319 +1012275 53 Inder J. Taneja https://numbers-magic.com; www.inderjtaneja.wordpress.com 26 and 2026 in Numbers and Magic Squares, Zenodo, December 22, 2025, pp. 1-74, https://doi.org/10.5281/zenodo.17944238 2. 704506 :=02026 ×101 +101 ×6202 0=22286 +682220 814517 :=12026 ×101 +101 ×6202 1=132286 +682231 924528 :=22026 ×101 +101 ×6202 2=242286 +682242 1034539 :=32026 ×101 +101 ×6202 3=352286 +682253 1144550 :=42026 ×101 +101 ×6202 4=462286 +682264 1254561 :=62026 ×101 +101 ×6202 5=572286 +682275 1364572 :=62026 ×101 +101 ×6202 6=682286 +682286 1474583 :=72026 ×101 +101 ×6202 7=792286 +682297 1584594 :=82026 ×101 +101 ×6202 8=902286 +682308 1694605 :=92026 ×101 +101 ×6202 9=1012286 +682319 We observe that not all the expressions are symmetric as expected. 24 Color Patterns 24.1 Three Color Patterns for 12 Month of 2026 24.1.1 Months 1 and 2 54 Inder J. Taneja https://numbers-magic.com; www.inderjtaneja.wordpress.com 26 and 2026 in Numbers and Magic Squares, Zenodo, December 22, 2025, pp. 1-74, https://doi.org/10.5281/zenodo.17944238 24.1.2 Months 3 and 4 24.1.3 Months 5 and 6 55 Inder J. Taneja https://numbers-magic.com; www.inderjtaneja.wordpress.com 26 and 2026 in Numbers and Magic Squares, Zenodo, December 22, 2025, pp. 1-74, https://doi.org/10.5281/zenodo.17944238 24.1.4 Months 7 and 8 24.1.5 Months 9 and 10 56 Inder J. Taneja https://numbers-magic.com; www.inderjtaneja.wordpress.com 26 and 2026 in Numbers and Magic Squares, Zenodo, December 22, 2025, pp. 1-74, https://doi.org/10.5281/zenodo.17944238 24.1.6 Months 11 and 12 24.2 Two Color Patterns for 20-26 Below are few two color patterns representing 20-26 in two colors. These are 180osymmetric. 57 Inder J. Taneja https://numbers-magic.com; www.inderjtaneja.wordpress.com 26 and 2026 in Numbers and Magic Squares, Zenodo, December 22, 2025, pp. 1-74, https://doi.org/10.5281/zenodo.17944238 These are double-digit bordered squares, where the magic square of orders 10 having a cornered magic square of order 6 in the middle. 25.9 Magic Squares of Order 11 Below are magic squares of order 11 with magic sums 26 and 2026. These are also cornered magic squares, where the magic square of orders 9 and 7 are cornered having magic square of ordedr 5 at the upper-left corner. The respective magic rectangles of orders 2×5,2×7 and 2×9are of equal sums in each case. 25.10 Magic Squares of Order 12 Below are magic squares of order 12 with magic sums 26 and 2026. 64 Inder J. Taneja https://numbers-magic.com; www.inderjtaneja.wordpress.com 26 and 2026 in Numbers and Magic Squares, Zenodo, December 22, 2025, pp. 1-74, https://doi.org/10.5281/zenodo.17944238 These are double-digit bordered squares, where the magic square of orders 12 and 8 having magic square of order 4 in the middle. The magic rectangles of order 2×4and 2×8are of equals sums in each case. 25.11 Upside-Down Magic Squares As we know that the the 0, 2 and 6 appearing in 26 and 2026 writing in digital form are upside-down, i.e., 180orotatable. 0 and 2 remains the same, but 6 becomes as 9. Below are few magic squares of orders 4 and 5 written in digital forms are upside-down. 25.11.1 Magic Squares of Order 4 •With Entry 26 Below is an upside-down magic square of order 4 having one of the entry as 26. See below an upside-down version of above magic square: 65 Inder J. Taneja https://numbers-magic.com; www.inderjtaneja.wordpress.com 26 and 2026 in Numbers and Magic Squares, Zenodo, December 22, 2025, pp. 1-74, https://doi.org/10.5281/zenodo.17944238 •With Entry 2026 Below is an upside-down magic square of order 4 having one of the entry as 2026. In this case a 180orotation give us a different magic square with different magic sum. 25.11.2 Magic Squares of Order 5 •With Entry 26 Below is an upside-down and pandiagonal magic square of order 5 having one of the entry as 26. 66 Inder J. Taneja https://numbers-magic.com; www.inderjtaneja.wordpress.com 26 and 2026 in Numbers and Magic Squares, Zenodo, December 22, 2025, pp. 1-74, https://doi.org/10.5281/zenodo.17944238 See below an upside-down version of above magic square: •With Entry 2026 Below is an upside-down and pandiagonal magic square of order 4 having one of the entry as 2026. In this case a 180orotation give us a different magic square with different magic sum. 67 Inder J. Taneja https://numbers-magic.com; www.inderjtaneja.wordpress.com 26 and 2026 in Numbers and Magic Squares, Zenodo, December 22, 2025, pp. 1-74, https://doi.org/10.5281/zenodo.17944238 •Author’s Contributions to Recreating Numbers and Magic Squares For author’s contribution to magic squares and recreation numbers please see the links below: •Inder J. Taneja, Magic Squares, 1. https://inderjtaneja.wordpress.com/2019/06/27/publications-magic-squares/ 2. https://numbers-magic.com/?p=668 •Inder J. Taneja, Recreation of Numbers, 1. https://inderjtaneja.wordpress.com/2019/06/27/publications-recreation-of-numbers/ 2. https://numbers-magic.com/?p=671 References •General References [1] Inder J. Taneja, 2019 In Numbers, Zenodo, December 31, 2019, Zenodo, pp. 1-27, http://doi.org/10.5281/zenodo.2529103. [2] Inder J. Taneja, 2020 In Numbers: Mathematical Style,Zenodo, December 31, 2019, pp. 1-37, http://doi.org/10.5281/zenodo.3596193. [3] Inder J. Taneja, Factorial-Type Numerical Calendar, Zenodo, March 24, 2020, pp. 1-33, http://doi.org/10.5281/zenodo.3726335. [4] Inder J. Taneja, Geometrical, Numerical, and Symmetrical Representations for the Days of 2020, Zenodo, October 04, 2020, pp. 1-201, http://doi.org/10.5281/zenodo.4065069. Also see the link: Inder J. Taneja, Geometrical, Numerical, and Symmetrical Representations for the Days of 2020 https://inderjtaneja.wordpress.com/2020/10/07/geometrical-numerical-and-symmetricalrepresentations-for-the-days-of-2020/ [5] Inder J. Taneja, Factorial-Type Numerical Calender 2021, Zenodo, December 16, 2020, pp. 1-31, http://doi.org/10.5281/zenodo.4329889. [6] Inder J. Taneja, 21 Mathematical Highlights for 2021, Zenodo, December 26, 2020, pp. 1-75, http://doi.org/10.5281/zenodo.4394408. [7] Inder J. Taneja, Geometrical, Numerical, and Symmetrical Representations for the Days of 2020, Zenodo, October 04, 2020, pp. 1-201, http://doi.org/10.5281/zenodo.4065069. 68 Inder J. Taneja https://numbers-magic.com; www.inderjtaneja.wordpress.com 26 and 2026 in Numbers and Magic Squares, Zenodo, December 22, 2025, pp. 1-74, https://doi.org/10.5281/zenodo.17944238 [8] Inder J. Taneja, Hardy-Ramanujan Number – 1729, Zenodo, December 22, 2021, pp. 1-106, https://doi.org/10.5281/zenodo.5799640. [9] Inder J. Taneja, Mathematical Beauty of 2022, Zenodo, December 26, 2021, pp. 1-78, https://doi.org/10.5281/zenodo.5805264. [10] Inder J. Taneja, Block-Wise and Block-Bordered Magic and Bimagic Squares with Magic Sums 21, 212and 2021, Zenodo, December 16, 2020, pp. 1-118, http://doi.org/10.5281/zenodo.4380343. [11] Inder J. Taneja, Fractional and Decimal Type Bordered Magic Squares With Magic Sum 2021, Zenodo, December 16, 2020, pp. 1-33, http://doi.org/10.5281/zenodo.4327333. [12] Inder J. Taneja, Block-Wise and Block-Bordered Magic Squares With Magic Sum 2022, Zenodo, December 28, 2021, pp. 1-38, https://doi.org/10.5281/zenodo.5807789. [13] Inder J. Taneja, 23 and 2023 in Numbers and Patterns, Zenodo, December 22, 2022, pp. 1-51, https://doi.org/10.5281/zenodo.7473340. [14] Inder J. Taneja, Mathematical Representations of the Last Day of the Year 23 Written American Style: 12.31.23 (123123), Zenodo, December 19, 2023, pp. 1-13, https://doi.org/10.5281/zenodo.10405771. [15] Inder J. Taneja, Mathematical Aspects of 24 and 2024, Zenodo, December 19, 2023, pp. 1-40, https://doi.org/10.5281/zenodo.10406530. [16] Inder J. Taneja, Reflexive Year 25: Mathematics of 25 and 2025 in Numbers and Magic Squares, Zenodo, December 20, 2024, pp. 1-94, https://doi.org/10.5281/zenodo.14533193. [17] Inder J. Taneja, Crazy, Single Digit, Single Letter and Pyramid-Type Representations for the Dates of the Year 25, Zenodo, March 12, 2025, pp. 1-388, https://doi.org/10.5281/zenodo.15013279. •Recreating Numbers [18] Inder J. Taneja, Crazy Sequential Representation: Numbers from 0 to 11111 in terms of Increasing and Decreasing Orders of 1 to 9, Jan. 2014, pp.1-161, http://arxiv.org/abs/1302.1479. [19] Inder J. Taneja, Semi-Selfie Numbers, Zenodo, February 12, 2019, pp. 1-394, http://doi.org/10.5281/zenodo.2562390. [20] Inder J. Taneja, Power-Type Semi-Selfie Numbers and Patterns, Zenodo, July 16, 2019, pp. 1-130, http://doi.org/10.5281/zenodo.3338366. 69 Inder J. Taneja https://numbers-magic.com; www.inderjtaneja.wordpress.com 26 and 2026 in Numbers and Magic Squares, Zenodo, December 22, 2025, pp. 1-74, https://doi.org/10.5281/zenodo.17944238 [21] Inder J. Taneja, Patterns in Selfie and Semi-Selfie Numbers, Zenodo, February 6, 2019, pp. 1-51, http://doi.org/10.5281/zenodo.2563202. [22] Inder J. Taneja, Single Digit Representations of Natural Numbers, Feb. 1015, pp.1-55, http://arxiv.org/abs/1502.03501. [23] Inder J. Taneja, Single Digit Representations of Natural Numbers From 1 to 5000, Zenodo, January 14, 2019, http://doi.org/10.5281/zenodo.2538893. [24] Inder J. Taneja, Patterned Selfie Fractions, Zenodo, October 27, 2019, pp. 1-267, http://doi.org/10.5281/zenodo.3520096. [25] Inder J. Taneja, Fixed Digits Repetitions Prime Patterns of Lengths 10, 9 and 8, Zenodo, February 8, 2019, pp. 1-175, http://doi.org/10.5281/zenodo.2560640. [26] Inder J. Taneja, Fixed Digits Repetitions Prime Patterns of Length 7, Zenodo, February 8, 2019, pp. 1-176,http://doi.org/10.5281/zenodo.2560668. [27] Inder J. Taneja, Fixed Digits Repetitions Prime Patterns of Length 6. Zenodo, February 9, 2019, pp. 1-303,http://doi.org/10.5281/zenodo.2561096. [28] Inder J. Taneja, Crazy Running Equality Expressions With Factorial and Square-Root, Zenodo, December 06, 2021, pp. 1-464,https://doi.org/10.5281/zenodo.5761752 •Universal and Upside-down Magic Squares [29] Inder J. Taneja, Intervally Distributed, Palindromic, Selfie Magic Squares, and Double Colored Patterns, RGMIA Research Report Collection, 18(2015), Art. 127, pp. 1-45. http://rgmia.org/papers/v18/v18a127.pdf. [30] Inder J. Taneja, Intervally Distributed, Palindromic and Selfie Magic Squares: Genetic Table and Colored Pattern – Orders 11 to 20, RGMIA Research Report Collection, 18(2015), Art. 140, pp. 1-43. http://rgmia.org/papers/v18/v18a140.pdf. [31] Inder J. Taneja, Intervally Distributed, Palindromic and Selfie Magic Squares – Orders 21 to 25 , 18(2015), Art. 151, pp. 1-33. http://rgmia.org/papers/v18/v18a151.pdf. [32] Inder J. Taneja, Multi-Digits Magic Squares, RGMIA Research Report Collection, 18(2015), Art. 159, pp. 1-22. http://rgmia.org/papers/v18/v18a159.pdf. [33] Inder J. Taneja, Magic Squares with Perfect Square Number Sums, Research Report Collection, 20(2017), Article 11, pp. 1-24, http://rgmia.org/papers/v20/v20a11.pdf. 70 Inder J. Taneja https://numbers-magic.com; www.inderjtaneja.wordpress.com 26 and 2026 in Numbers and Magic Squares, Zenodo, December 22, 2025, pp. 1-74, https://doi.org/10.5281/zenodo.17944238 [34] Inder J. Taneja, Pythagorean Triples and Perfect Square Sum Magic Squares, RGMIA Research Report Collection, 20(2017), Art. 128, pp. 1-22, http://rgmia.org/papers/v20/v20a128.pdf. [35] Inder J. Taneja, Selfie Palindromic Magic Squares, RGMIA Research Report Collection, 18(2015), Art. 98, pp. 1-15. .http://rgmia.org/papers/v18/v18a98.pdf. [36] Inder J. Taneja, Block-Wise Equal Sums Pandiagonal Magic Squares of Order 4k,Zenodo, Open Access, January 31, 2019, pp. 1-17, http://doi.org/10.5281/zenodo.2554288. [37] Inder J. Taneja, Block-Wise Equal Sums Magic Squares of Orders 3kand 6k, , Zenodo, Open Access, Febuary 01, 2019, pp. 1-55 http://doi.org/10.5281/zenodo.2554895. [38] Inder J. Taneja, Block-Wise Unequal Sums Magic Squares, Zenodo, Open Access, Febuary 01, 2019, pp. 1-55, http://doi.org/10.5281/zenodo.2555260. [39] Inder J. Taneja, Magic Rectangles in Construction of Block-Wise Pandiagonal Magic Squares, Zenodo, Open Access, January 31, 2019, pp. 1-49 , http://doi.org/10.5281/zenodo.2554520. [40] Inder J. Taneja, Magic Crosses: Repeated and Non Repeated Entries, Zenodo, Open Access, Open Access, Febuary 01, 2019, pp. 1-37, http://doi.org/10.5281/zenodo.2554623. [41] Inder J. Taneja, Representations of Letters and Numbers With Equal Sums Magic Squares of Orders 4 and 6, Zenodo, Open Access, Febuary 01, 2019, pp. 1-82, http://doi.org/10.5281/zenodo.2555287. [42] Inder J. Taneja, Block-Wise Magic and Bimagic Squares of Orders 12 to 36, Zenodo, Febuary 01, 2019, pp. 1-53, http://doi.org/10.5281/zenodo.2555343. [43] Inder J. Taneja, Different Digits Magic Squares and Number Patterns, Zenodo, Febuary 01, 2019, pp. 1-34, http://doi.org/10.5281/zenodo.2555327. [44] Inder J. Taneja, Palindromic, Patterned Magic Sums, Composite, and Colored Patterns in Magic Squares, RGMIA Research Report Collection, 21(2018), Art. 19, pp. 1-81, http://rgmia.org/papers/v21/v21a19.pdf. Also revised in Zenodo, February 2, 2019, pp. 1-99, http://doi.org/10.5281/zenodo.2555741. •Striped Magic Squares [45] Inder J. Taneja, Striped Magic Squares of Even Orders 6, 8, 10, 12 and 14, Zenodo, November 10, 2023, pp. 1-34, https://doi.org/10.5281/zenodo.10107355. [46] Inder J. Taneja, Striped Magic Squares of 12 – Revised, Zenodo, September 07, 2024, pp. 1-30, https://zenodo.org/records/13725031. 71 Inder J. Taneja https://numbers-magic.com; www.inderjtaneja.wordpress.com 26 and 2026 in Numbers and Magic Squares, Zenodo, December 22, 2025, pp. 1-74, https://doi.org/10.5281/zenodo.17944238 [47] Inder J. Taneja, Striped Magic Squares of 16 – Revised, Zenodo, September 07, 2024, pp. 1-39, https://doi.org/10.5281/zenodo.13720366. [48] Inder J. Taneja, Striped Magic Squares of 18, Zenodo, June 13, 2024, pp. 1-34, https://doi.org/10.5281/zenodo.11629567. [49] Inder J. Taneja, Striped Magic Squares of 20, Zenodo, August 24, 2024, pp. 1-34, https://doi.org/10.5281/zenodo.11629567. •Double Digits Magic Squares [50] Inder J. Taneja, Two Digits Bordered Magic Squares Multiples of 4: Orders 8 to 24, Zenodo, April, 26, 2023, pp. 1-43, https://doi.org/10.5281/zenodo.7866956. [51] Inder J. Taneja, Two Digits Bordered Magic Squares of Orders 28 and 32, Zenodo, April, 26, 2023, pp. 1-36, https://doi.org/10.5281/zenodo.7866981. [52] Inder J. Taneja, Two Digits Bordered Magic Squares of Orders 10, 14, 18 and 22, Zenodo, April, 30, 2023, pp. 1-43, https://doi.org/10.5281/zenodo.7880931. [53] Inder J. Taneja, Two Digits Bordered Magic Squares of Orders 26 and 30, Zenodo, April, 30, 2023, pp. 1-45, https://doi.org/10.5281/zenodo.7880937. [54] Inder J. Taneja, Two Digits Bordered Magic Squares of Orders 36 and 40, Zenodo, May, 04, 2023, pp. 1-41, https://doi.org/10.5281/zenodo.7896709. [55] Inder J. Taneja, Two Digits Bordered Magic Squares of Orders 34 and 38, Zenodo, May 10, 2023, pp. 1-45, https://doi.org/10.5281/zenodo.7922571. [56] Inder J. Taneja, New Concepts in Magic Squares: Double Digits Bordered Magic Squares of Orders 7 to 108, Zenodo, August 09, 2023, pp. 1-30, https://doi.org/10.5281/zenodo.8230214. •Cornered Magic Squares [57] Inder J. Taneja, Cornered Magic Squares of Order 6, Zenodo, May 23, 2023, pp. 1-23, https://doi.org/10.5281/zenodo.7960679. [58] Inder J. Taneja, Cornered Magic Squares of Orders 5 to 13, Zenodo, June 03, 2023, pp. 1-71, https://doi.org/10.5281/zenodo.8000467. 72 Inder J. Taneja https://numbers-magic.com; www.inderjtaneja.wordpress.com 26 and 2026 in Numbers and Magic Squares, Zenodo, December 22, 2025, pp. 1-74, https://doi.org/10.5281/zenodo.17944238 [59] Inder J. Taneja, Cornered Magic Squares of Orders 14 to 24, Zenodo, June 03, 2023, pp. 1-39, https://doi.org/10.5281/zenodo.8000471. [60] Inder J. Taneja, New Concepts in Magic Squares: Cornered Magic Squares of Orders 5 to 81, Zenodo, August 09, 2023, pp. 1-27, https://doi.org/10.5281/zenodo.8231157. ————————————————- 73