The smallest squares containingk 95's :
17956 = 134²,   4959529 = 2227²,   9559559529 = 97773²,
13095959519556 = 3618834²,   9595954709595136 = 97958944².

95² = 9025, 9=3² and 25=5².

95² = 9025, a square with different digits.

95² = 9025, 9 + 0 + 2 + 5 = 4².

95² = 20³ + 4⁵ + 1⁷.

A 3-by-3 magic square consisting of different squares with constant 95²:

152^k + 209^k + 3344^k + 5320^k are squares for k = 1,2,3 (95², 6289², 433561²).
513^k + 1292^k + 3382^k + 3838^k are squares for k = 1,2,3 (95², 5301², 312265²).
960^k + 2080^k + 2745^k + 3240^k are squares for k = 1,2,3 (95², 4825², 254125²).

Komachi Fractions : (21/95)² = 7938/162450, (13/95)² = 9126/487350.

Komachi equations:
95² = - 1 - 2 + 3 * 45 * 67 - 8 - 9 = 9 - 8 - 7 + 6 - 5 + 43 * 210
95² = - 9 - 8 + 7 * 6 * 5 * 43 + 2 + 10 = - 9 + 8 + 7 - 6 - 5 + 43 * 210,
95² = - 9² + 8² * 7² + 65² + 43² - 2² - 10².

(95² + 5) = (9² + 5)(10² + 5).

(1 + 2)(3 + 4 + ... + 32)(33 + 34 + ... + 95) = 2520²,
(1 + 2 + ... + 6)(7 + 8 + ... + 32)(33 + 34 + ... + 95) = 6552²,
(1 + 2 + ... + 8)(9 + 10 + ... + 20)(21 + 22 + ... + 95) = 5220²,
(1 + 2 + ... + 11)(12 + 13 + ... + 32)(33 + 34 + ... + 95) = 11088²,
(1 + 2 + ... + 21)(22 + 23 + ... + 32)(33 + 34 + ... + 95) = 16632²,
(1 + 2 + ... + 25)(26 + 27 + ... + 30)(31 + 32 + ... + 95) = 13650²,
(1 + 2 + ... + 27)(28 + 29 + ... + 32)(33 + 34 + ... + 95) = 15120²,
(1 + 2 + ... + 35)(36 + 37 + ... + 39)(40 + 41 + ... + 95) = 18900²,
(1 + 2 + ... + 47)(48)(49 + 50 + ... + 95) = 13536².

(1² + 2² + ... + 15²)(16² + 17² + ... + 64²)(65² + 66² + ... + 95²) = 4687200².

(1³ + 2³ + ... + 10³)(11³ + 12³ + ... + 24³)(25³ + 26³ + ... + 95³) = 73804500².

95⁸ = 6634204312890625,
    6 + 6 + 3 + 4 + 20 + 43 + 12 + 8906 + 25 = 6 + 6 + 3 + 42 + 04 + 31 + 2 + 8906 + 25
  = 6 + 6 + 3 + 42 + 043 + 12 + 8906 + 2 + 5 = 6 + 6 + 34 + 2 + 043 + 1 + 2 + 8906 + 25
  = 6 + 6 + 34 + 20 + 43 + 1 + 2 + 8906 + 2 + 5 = 6 + 63 + 4 + 2 + 04 + 3 + 12 + 8906 + 25
  = 6 + 63 + 4 + 2 + 04 + 31 + 2 + 8906 + 2 + 5 = 6 + 63 + 4 + 20 + 4 + 3 + 12 + 8906 + 2 + 5
  = 66 + 3 + 4 + 2 + 04 + 3 + 12 + 8906 + 25 = 66 + 3 + 4 + 2 + 04 + 31 + 2 + 8906 + 2 + 5
  = 66 + 3 + 4 + 20 + 4 + 3 + 12 + 8906 + 2 + 5 = 66 + 34 + 2 + 04 + 3 + 1 + 2 + 8906 + 2 + 5
  = 95².

95² = 9025 appears in the decimal expressions of π and e:
  π = 3.14159•••9025••• (from the 5392nd digit),
  e = 2.71828•••9025••• (from the 408th digit),
  (9025 is the 4th 4-digit square in the expression of e.)

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Page of Squares : First Upload March 22, 2004 ; Last Revised February 3, 2011
by Yoshio Mimura, Kobe, Japan