The smallest squares containing k 23's :
2304 = 48²,   232324 = 482²,   2390623236 = 48894²,
2391232342321 = 1546361²,   14623123112323236 = 120926106².

The first integer which is the sum of 8 squares in just two ways (see 20).

Every integer greater than 23 is the sum of 10 nonzero squares.

23² = 529, 5 + 2 + 9 = 4².

23² = 529 is a zigzag square.

23² = 1³ + 2³ + 2³ + 8³ = 1⁴ + 2⁴ + 4⁴ + 4⁴.

(4² + 3)(5² + 3) = 23² + 3,
(5² - 7)(6² - 7) = 23² - 7,
(1² + 3)(2² + 3)(4² + 3) = 23² + 3,
(3² - 7)(4² - 7)(6² - 7) = 23² - 7.

(1 + 2)(3 + ... + 15)(16 + ... + 23) = 234²,
(1 + 2 + ... + 4)(5 + 6 + ... + 16)(17 + ... + 23) = 420²,
(1 + 2 + ... + 10)(11 + 12 + ... + 21)(22 + 23) = 660²,
(1 + 2 + ... + 11)(12)(13 + 14 + ... + 23) = 396²,
(1 + 2 + ... + 11)(12 + 13 + ... + 20)(21 + 22 + 23) = 792².

(1³ + 2³ + 3³ + 4³ + 5³ + 6³)(7³ + 8³ + ... + 20³)(21³ + 22³ + 23³) = 785862².

Komachi Fractions : 23² = 385641/729, (23/315)² = 4761/893025.

Komachi: 23² = 12 - 34 * 5 + 678 + 9 and more 17 equations.
Komachi: 23² = 9 + 87 + 6 - 5 + 432 * 1 and more 39 equations.

23² = (1⁴ + 2² + 3³) + (4⁴ + 5² + 6³).

The sum of consecutive primes 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 = 10²

None of the binomial coefficients _nC_k are square-free for every integer n > 23.

In the set {23, 1346, 4738, 8258} the sum of any two numbers is a square.

1² + 2² + 3² + ... + 23² = 4324, which consists of digits < 5.

23² = 529, 5 + 2 * 9 = 23.

23 is the first prime p for which the Legendre symbol (a/p) = 1 for a = 1,2,3,4.

23² = 529 appears in the decimal expressions of π and e:
  π = 3.14159•••529••• (from the 1058th digit),
(529 is the 9th 3-digit square in the expr. of π,)
  e = 2.71828•••529••• (from the 1265th digit).