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92

The smallest squares containingk 92's :
5929 = 772,   929296 = 9642,   792929281 = 281592,
920492492929 = 9594232,   9292589249297929 = 963980772.

92 is the third integer which is the sum of 5 squares in just 6 ways.

922 = 72 + 82 + 92 + 102 + ... + 292.

922 = 8464, a zigzag square with even digits.

922 = 8464, 8 * 46 / 4 = 92.

922± 3 are primes.

922 = (42 + 7)(192 + 7).

922 is the 5th square which is the sum of 3 distinct squares in just 3 ways:
    122 + 242 + 882 = 122 + 562 + 722 = 242 + 522 + 722.

922 = 24 + 44 + 84 + 84.

928 = 5132188731375616, 5 + 1 + 3 + 2 + 1 + 8 + 873 + 1 + 3 + 7561 + 6 = 922,
    5 + 132 + 18 + 8 + 731 + 3 + 7561 + 6 = 51 + 3 + 21 + 88 + 731 + 3 + 7561 + 6
  = 51 + 321 + 8 + 8 + 7313 + 756 + 1 + 6 = 51 + 321 + 88 + 7313 + 75 + 616
  = 513 + 2188 + 7 + 3 + 137 + 5616 = 5132 + 1887 + 3 + 1375 + 61 + 6 = 922.

667k + 2507k + 2553k + 2737k are squares for k = 1,2,3 (922, 45542, 2306442)./p>

Komachi Fractions : 922 = 1980576/234 = 2970864/351.

Komachi equations:
922 = - 12 - 22 / 32 + 42 * 52 / 62 * 72 + 892 = 982 + 72 * 62 - 542 + 32 + 22 - 12
  = 982 - 72 * 62 - 52 * 42 + 322 */ 12 = 92 + 872 - 62 + 52 * 42 + 32 + 212,
922 = 94 - 84 - 74 - 64 - 54 + 44 + 34 - 24 + 104.

(922 + 2) = (92 + 2)(102 + 2),
(922 + 6) = (22 + 6)(292 + 6) = (12 + 6)(42 + 6)(72 + 6).

4402 = 602 + 612 + 622 + ... + 922.

12 + 22 + 32 + 42 + ... + 922 = 263810, which consists of different digits.

(1 + 2 + ... + 8)(9 + 10 + 11 + 12)(13 + 14 + ... + 92) = 25202,
(1 + 2 + ... + 17)(18 + 19 + ... + 67)(68 + 69 + ... + 92) = 255002,
(1 + 2 + ... + 40)(41 + 42 + ... + 82)(83 + 84 + ... + 92) = 430502,
(1 + 2 + ... + 50)(51 + 52 + ... + 75)(76 + 77 + ... + 92) = 535502.

(13 + 23 + 33)(43 + ... + 123)(133 + ... + 923) = 19958402.

(12 + 22 + 32)(42 + ... + 142)(152 + ... + 402)(412 + ... + 922) = 84584502,
(12 + 22 + 32 + 42)(52 + ... + 352)(362 + ... + 602)(612 + ... + 922) = 706800002,
(12 + ... + 622)(632)(642 + ... + 802)(812 + ... + 922) = 16036083002.

922 = 8464 appears in the decimal expressions of π and e:
  π = 3.14159•••8464••• (from the 6330th digit),
  e = 2.71828•••8464••• (from the 8500th digit).


Page of Squares : First Upload March 15, 2004 ; Last Revised January 13, 2014
by Yoshio Mimura, Kobe, Japan