The smallest squares containingk 94's :
9409 = 97²,   9449476 = 3074²,   3949494025 = 62845²,
1949407948944 = 1396212²,   69994942945949476 = 264565574².

94² = 8836, 8 + 8 + 3 + 6 = 5².

94² is the first square which is the sum of 8 fourth powers in just 2 ways :[1,4,4,4,4,5,5,9], [1,5,5,6,6,6,6,7].

141^k + 1645^k + 2773^k + 4277^k are squares for k = 1,2,3 (94², 5358², 322514²).
517^k + 893^k + 3525^k + 3901^k are squares for k = 1,2,3 (94², 5358², 322514²).

Komachi equations:
94² = 98 / 7 * 654 - 32 * 10,
94² = - 1² + 23² + 4² * 5² + 6² - 7² + 89² = 9² - 87² - 6² - 5² + 4² * 32² + 1²
  = - 9² + 87² + 6² * 5² + 4² - 3² + 21².

94⁸ = 6095689385410816, 6 + 095 + 6 + 8 + 93 + 8541 + 081 + 6 = 94².

(94² + 4) = (1² + 4)(42² + 4) = (3² + 4)(26² + 4) = (9² + 4)(10² + 4)
  = (2² + 4)(3² + 4)(9² + 4),
(94² + 8) = (2² + 8)(27² + 8).

94² = (1² + 2² + 3² + ... + 21²) + (1² + 2² + 3² + ... + 25²).

(1 + 2)(3 + 4 + ... + 66)(67 + 68 + ... + 94) = 3864²,
(1 + 2 + 3)(4 + 5 + ... + 87)(88 + 89 + ... + 94) = 3822²,
(1 + 2 + ... + 12)(13)(14 + 15 + ... + 94) = 2106²,
(1 + 2 + ... + 12)(13 + 14 + ... + 87)(88 + 89 + ... + 94) = 13650²,
(1 + 2 + ... + 15)(16 + 17 + ... + 59)(60 + 61 + ... + 94) = 23100²,
(1 + 2 + ... + 35)(36 + 37 + ... + 55)(56 + 57 + ... + 94) = 40950²,
(1 + 2 + ... + 51)(52 + 53 + ... + 77)(78 + 79 + ... + 94) = 57018²,
(1 + 2 + ... + 72)(73)(74 + 75 + ... + 94) = 18396².

(1² + 2²)(3² + 4² + ... + 9²)(10² + 11² + ... + 38²)(39² + 40² + ... + 94²) = 2622760²,
(1² + 2² + ... + 5²)(6² + 7² + ... + 11²)(12²)(13² + 14² + ... + 94²) = 1001220²,
(1² + 2² + ... + 5²)(6² + 7² + ... + 38²)(39²)(40² + 41² + ... + 94²) = 20338890².

94² = 8836 appears in the decimal expressions of π and e:
  π = 3.14159•••8836••• (from the 13924th digit),
  e = 2.71828•••8836••• (from the 16958th digit).

---

Page of Squares : First Upload March 15, 2004 ; Last Revised February 3, 2011
by Yoshio Mimura, Kobe, Japan