The smallest squares containing k 26's :
2601 = 51²,   26265625 = 5125²,   262699264 = 16208²,
26262632085264 = 5124708²,   2626526112626025 = 51249645².

The 3rd integer which is the sum of 3 distinct squares: 1² + 3² + 4².

The 2nd integer which is the sum of 8 squares in just 2 ways (see 24).

The first integer which is the sum of m squares for m = 2, 3, .. , 12.

26² = 676, 6² + 7² + 6² = 11².

26² = 676 is a palindromic and zigzag square.

The sum of the squares of the divisors of 24 is equal to the sum of the squares of the divisors of 26.

26² is the 5th square which is the sum of 6 fourth powers : 1⁴ + 1⁴ + 3⁴ + 3⁴ + 4⁴ + 4⁴.
26² is the first square which is the sum of 7 fourth powers : 1⁴ + 1⁴ + 1⁴ + 2⁴ + 2⁴ + 2⁴ + 5⁴.

26^k + 338^k + 910^k + 1226^k are squares for k = 1,2,3 (50², 1564², 51332²).
46^k + 170^k + 202^k + 258^k are squares for k = 1,2,3 (26², 372², 5516²).

26⁶ = 308915776, 3 + 089 + 1 + 577 + 6 = 26²
26⁸ = 208827064576, 2 + 08 + 8 + 2 + 70 + 6 + 4 + 576 = 26².
26¹⁰ = 141167095653376, 1 + 4 + 1 + 1 + 6 + 7 + 09 + 565 + 3 + 3 + 76 = 26² and more 23 equations.

Komachi Fractions : (19/26)² = 48735/91260, (25/26)² = 84375/91260.

Komachi equations:
26² = 1 * 2 * 345 - 6 - 7 + 8 - 9 = 12 + 3 * 4 * 56 - 7 + 8 - 9 = 1 + 234 + 56 * 7 / 8 * 9, and more 31 equations, 26² = 98 * 7 + 6 - 5 - 4 - 3 * 2 - 1 = 98 * 7 + 6 - 5 - 4 * 3 + 2 - 1 = 98 * 7 + 6 - 5 * 4 + 3 + 2 - 1, and more 32 equations, 26² = 98 * 7 + 6 + 5 - 4 + 3 - 2 * 10 = 98 * 7 + 6 - 5 + 4 - 3 - 2 - 10 = 98 * 7 + 6 - 5 + 4 - 3 / 2 * 10, and more 26 equations,
26² = 1² - 23² * 4² + 56² + 78² - 9².

2² + 5² + 8² + 11² + 14² + 17² + 20² + 23² + 26² = 48²

1² + 2² + 3² + ... + 26² = 6201, which consists of different digits.

(26² + 4) = (2² + 4)(9² + 4),   (26² - 4) = (5² - 4)(6² - 4),
(26² + 6) = (4² + 6)(5² + 6),   (26² + 8) = (2² + 8)(7² + 8).

(1)(2 + 3 + ... + 8)(9 + 10 + ... + 26) = 105²,
(1 + 2 + ... + 5)(6 + 7 + 8 )(9 + 10 + ... + 26) = 315²,
(1 + 2 + ... + 6)(7 + 8)(9 + 10 + ... + 26) = 315²,
(1 + 2 + ... + 6)(7 + 8 + ... + 15)(16 + 17 + ... + 26) = 693²,
(1 + 2 + ... + 9)(10 + 11 + ... + 24)(25 + 26) = 765²,
(1 + 2 + ... + 17)(18 + 19 + ... + 24)(25 + 26) = 1071²,
(1 + 2 + ... + 14)(15 + 16 + ... + 21)(22 + 23 + ... + 26) = 1260².

1³ + 2³ + 3³+ 4³+ ... + 26³ = (1 + 2 + 3 + 4 + ... + 26)² = 351²,
(1³ + 2³ + ... + 12³)(13³ + 14³ + ... + 17³)(18³ + 19³ + ... + 26³) = 3243240².

26² = 676 appears in the decimal expressions of π and e:
  π = 3.14159•••676••• (from the 590th digit), (676 is the 4th 3-digit square in the expr. of π)
  e = 2.71828•••676••• (from the 59th digit), (676 is the first 3-digit square in the expr. of e).

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Page of Squares : First Upload October 27, 2003 ; Last Revised January 25, 2011
by Yoshio Mimura, Kobe, Japan