The smallest squares containingk 76's :
576 = 24²,   76176 = 276²,   2447676676 = 49474²,
7628776576576 = 2762024²,   3876819767676769 = 62264113².

The squares which begin with 76 and end in 76 are
76176 = 276²,   763876 = 874²,   767376 = 876²,   7695076 = 2774²,
76108176 = 8724²,...

76 appears in its square : 76² = 5776.

76176 = 276², a square.

76² = 5776, 5 + 7 + 7 + 6 = 5²,
76² = 5776, 5 + 77 - 6 = 76,
76² = 5776, 57² + 76² = 95².

76² = 2! + 2! + 3! + 3! + 6! + 7!.

76² = 5776, a square with odd digits except the last digit.

76176 = 276².

Cubic Polynomial : (X + 76²)(X + 192²)(X + 513²) = X³ + 553²X² + 106932²X + 7485696².

Komachi equations: 76² = 1 + 23 * 4 * 56 + 7 * 89 = 9 + 8 * 7 * 6 + 5432 - 1,
76² = 1² - 2² * 3² - 45² - 6² - 7² + 89² = - 1² - 2² * 3² * 4² + 56² + 7² * 8² + 9²
  = - 12² - 3² * 4² + 5² + 6² + 78² - 9² = 9² + 8² + 76² - 5² + 4² - 3² * 2² - 10²
  = 9² * 8² - 7² + 65² + 4² - 3² * 2² * 10² = - 9² - 8² + 76² + 5² - 4² + 3² * 2² + 10²
  = - 9² - 8² - 7² + 65² + 43² - 2² - 10².

(76² + 2) = (2² + 2)(31² + 2),   (76² + 4) = (8² + 4)(9² + 4),
(76² - 8) = (4² - 8)(27² - 8).

76² + 77² + 78² + ... + 99² = 430².

76⁸ = 1113034787454976, 1 + 1 + 1 + 3 + 034 + 7 + 8 + 745 + 4976 = 76²,
    1 + 1 + 1 + 30 + 3 + 4 + 7 + 8 + 745 + 4976 = 1 + 1 + 1 + 303 + 478 + 7 + 4 + 5 + 4976
  = 1 + 1 + 130 + 3 + 47 + 87 + 4 + 5497 + 6 = 1 + 113 + 03 + 4 + 78 + 74 + 5497 + 6
  = 11 + 130 + 3 + 47 + 8 + 74 + 5497 + 6 = 11 + 130 + 34 + 7 + 87 + 4 + 5497 + 6
  = 111 + 3 + 03 + 4 + 78 + 74 + 5497 + 6 = 111 + 30 + 3 + 47 + 8 + 74 + 5497 + 6
  = 111 + 30 + 34 + 7 + 87 + 4 + 5497 + 6 = 1113 + 03 + 4 + 7 + 87 + 4549 + 7 + 6 = 76².

(1)(2 + 3 + 4)(5 + 6 + ... + 76) = 162²,
(1)(2 + 3 + ... + 25)(26 + 27 + ... + 76) = 918²,
(1 + 2)(3 + 4 + ... + 51)(52 + 53 + ... + 76) = 2520²,
(1 + 2 + ... + 8)(9 + 10 + ... + 25)(26 + 27 + ... + 76) = 5202²,
(1 + 2 + ... + 12)(13 + 14 + ... + 51)(52 + 53 + ... + 76) = 12480²,
(1 + 2 + ... + 26)(27)(28 + 29 + ... + 76) = 4914²,
(1 + 2 + ... + 26)(27 + 28 + ... + 51)(52 + 53 + ... + 76) = 23400²,
(1 + 2 + ... + 48)(49 + 50 + 51)(52 + 53 + ... + 76) = 16800²,
(1 + 2 + ... + 50)(51)(52 + 53 + ... + 76) = 10200²,
(1 + 2 + ... + 72)(73)(74 + 75 + 76) = 6570².

(1² + 2²)(3² + 4² + ... + 9²)(10² + 11² + ... + 34²)(35² + 36² + ... + 76²) = 1594600²,
(1² + 2² + ... + 4²)(5² + 6² + ... + 18²)(19² + 20² + ... + 38²)(39² + 40² + ... + 76²) = 11718630²,
(1² + 2² + ... + 12²)(13² + 14² + ... + 39²)(40² + 41² + ... + 50²)(51² + 52² + ... + 76²) = 175396650².

76² = 5776 appears in the decimal expressions of π and e:
  π = 3.14159•••5776••• (from the 19710th digit),
  e = 2.71828•••5776••• (from the 6237th digit).

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Page of Squares : First Upload February 23, 2004 ; Last Revised August 4, 2013
by Yoshio Mimura, Kobe, Japan