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7800 - 7899

7800

78002 = (112 - 1)(142 - 1)(512 - 1) = (32 - 1)(42 - 1)(142 - 1)(512 - 1).

78002 = 53 + 1153 + 3903.

Page of Squares : First Upload June 2, 2008 ; Last Revised January 11, 2014
by Yoshio Mimura, Kobe, Japan

7803

78032 = 1533 + 3063 + 3063.

Page of Squares : First Upload June 2, 2008 ; Last Revised June 2, 2008
by Yoshio Mimura, Kobe, Japan

7808

78082 = 60964864, and 60 * 96 + 4 * 8 * 64 = 7808.

78082 = 2253 + 2873 + 2963 = 244 + 244 + 244 + 884 = 45 + 125 + 125 + 365.

Page of Squares : First Upload June 2, 2008 ; Last Revised June 2, 2008
by Yoshio Mimura, Kobe, Japan

7810

78102 = 60996100.

Page of Squares : First Upload June 2, 2008 ; Last Revised June 2, 2008
by Yoshio Mimura, Kobe, Japan

7811

78112 = 93 + 1743 + 3823 = 1093 + 2233 + 3653.

78115 = 29075901506271560051 :
22 + 92 + 02 + 72 + 52 + 92 + 02 + 12 + 52 + 02 + 622 + 72 + 12 + 52 + 602 + 02 + 52 + 12 = 7811.

Page of Squares : First Upload June 2, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

7812

78122 = 663 + 2103 + 3723 = 1263 + 2363 + 3583.

Page of Squares : First Upload June 2, 2008 ; Last Revised June 2, 2008
by Yoshio Mimura, Kobe, Japan

7813

78132 = 61042969, and 61 + 0 + 4 * 2 * 969 = 7813.

Page of Squares : First Upload June 2, 2008 ; Last Revised June 2, 2008
by Yoshio Mimura, Kobe, Japan

7815

78152 = 323 + 703 + 3933.

Page of Squares : First Upload June 2, 2008 ; Last Revised June 2, 2008
by Yoshio Mimura, Kobe, Japan

7816

78162 = 61089856, and 6 + 10 * 8 * 98 - 5 * 6 = 7816.

Page of Squares : First Upload June 2, 2008 ; Last Revised June 2, 2008
by Yoshio Mimura, Kobe, Japan

7818

78182 = 61121124, and 62 + 12 + 12 + 22 + 12 + 12 + 22 + 42 = 82.

78182 = 2053 + 2823 + 3113.

Page of Squares : First Upload June 2, 2008 ; Last Revised June 2, 2008
by Yoshio Mimura, Kobe, Japan

7819

78192 = 61136761, and 62 + 12 + 12 + 32 + 62 + 72 + 62 + 12 = 132.

Page of Squares : First Upload June 2, 2008 ; Last Revised June 2, 2008
by Yoshio Mimura, Kobe, Japan

7820

78202 = 693 + 1423 + 3873 = 1963 + 2103 + 3543.

Page of Squares : First Upload June 2, 2008 ; Last Revised June 2, 2008
by Yoshio Mimura, Kobe, Japan

7823

78232 = 164 + 264 + 294 + 884.

Page of Squares : First Upload June 2, 2008 ; Last Revised June 2, 2008
by Yoshio Mimura, Kobe, Japan

7824

78242 = 263 + 1663 + 3843.

Page of Squares : First Upload June 2, 2008 ; Last Revised June 2, 2008
by Yoshio Mimura, Kobe, Japan

7825

78252 = 303 + 1853 + 3803 = 2003 + 2303 + 3453.

Page of Squares : First Upload June 2, 2008 ; Last Revised June 2, 2008
by Yoshio Mimura, Kobe, Japan

7826

Komachi equation: 78262 = 982 / 72 * 652 * 432 * 22 / 102.

Page of Squares : First Upload November 9, 2010 ; Last Revised November 9, 2010
by Yoshio Mimura, Kobe, Japan

7827

78272 = 61261929, and 6 * 1261 + 9 * 29 = 7827.

78272 = 13 + 2403 + 3623 = 1463 + 2893 + 3243 = 1593 + 2053 + 3653.

Page of Squares : First Upload June 2, 2008 ; Last Revised June 2, 2008
by Yoshio Mimura, Kobe, Japan

7828

78285 = 29393688331265594368 :
22 + 92 + 392 + 32 + 62 + 82 + 82 + 332 + 122 + 62 + 52 + 52 + 92 + 42 + 32 + 682
= 292 + 32 + 92 + 32 + 62 + 82 + 82 + 332 + 122 + 62 + 52 + 592 + 432 + 62 + 82
= 22 + 92 + 392 + 32 + 682 + 82 + 332 + 122 + 62 + 52 + 52 + 92 + 42 + 32 + 62 + 82 = 7828.

Page of Squares : First Upload December 8, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

7830

78302 = (32 + 9)(362 + 9)(512 + 9) = (32 + 9)(62 + 9)(72 + 9)(362 + 9)
= (62 + 9)(92 + 9)(1232 + 9) = (52 + 5)(202 + 5)(712 + 5).

78305 = 29431256946414300000 :
292 + 432 + 12 + 22 + 562 + 92 + 42 + 62 + 42 + 12 + 432 + 02 + 02 + 02 + 02 + 02 = 7830.

Page of Squares : First Upload December 8, 2008 ; Last Revised January 11, 2014
by Yoshio Mimura, Kobe, Japan

7831

1 / 7831 = 0.00012769.... and 12769 = 1132.

78314 = 3760701781842721,
and 32 + 762 + 02 + 72 + 02 + 12 + 72 + 82 + 12 + 82 + 422 + 72 + 22 + 12 = 7831.

78315 = 29450055653610348151 :
22 + 92 + 42 + 502 + 02 + 52 + 52 + 62 + 52 + 362 + 12 + 02 + 342 + 82 + 12 + 512 = 7831.

Page of Squares : First Upload June 2, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

7833

78332± 2 are primes.

78332 = 683 + 703 + 3933.

Page of Squares : First Upload June 2, 2008 ; Last Revised January 11, 2014
by Yoshio Mimura, Kobe, Japan

7835

78352 = 1643 + 2573 + 3423.

Page of Squares : First Upload June 2, 2008 ; Last Revised June 2, 2008
by Yoshio Mimura, Kobe, Japan

7837

78375 = 29563049723326822957 :
292 + 562 + 32 + 02 + 492 + 72 + 22 + 32 + 32 + 262 + 82 + 222 + 92 + 52 + 72 = 7837.

Page of Squares : First Upload December 8, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

7839

78392 = 23 + 1693 + 3843.

Page of Squares : First Upload June 2, 2008 ; Last Revised June 2, 2008
by Yoshio Mimura, Kobe, Japan

7840

78402± 3 are primes.

78402 = 61465600, and 6 * 14 / 6 * 560 + 0 = 7840.

78402 = 923 + 1963 + 3763 = 1963 + 2523 + 3363.

Page of Squares : First Upload June 2, 2008 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

7841

78412 = 61481281, and 61 + 4 + 8 * 12 * 81 = 7841.

Page of Squares : First Upload June 2, 2008 ; Last Revised June 2, 2008
by Yoshio Mimura, Kobe, Japan

7844

78442± 3 are primes.

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

7847

78472 = 143 + 2443 + 3613 = 1333 + 2253 + 3633.

Page of Squares : First Upload June 2, 2008 ; Last Revised June 2, 2008
by Yoshio Mimura, Kobe, Japan

7848

78482 = 383 + 723 + 3943.

Page of Squares : First Upload June 2, 2008 ; Last Revised June 2, 2008
by Yoshio Mimura, Kobe, Japan

7851

78515 = 29828051674576264251 :
292 + 82 + 22 + 802 + 52 + 162 + 72 + 42 + 52 + 72 + 62 + 22 + 62 + 42 + 22 + 52 + 12 = 7851.

Page of Squares : First Upload December 8, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

7854

78542 = 313 + 1973 + 3783.

The integral triangle of sides 3367, 37246, 37995 has square area 78542.

Page of Squares : First Upload June 2, 2008 ; Last Revised October 18, 2011
by Yoshio Mimura, Kobe, Japan

7857

Loop of length 56 by the function f(N) = ... + c2 + b2 + a2 where N = ... + 1002c + 100b + a:
7857 - 9333 - 9738 - 10853 - ... - 12017 - 690 - 8136 - 7857
(Note f(7857) = 782 + 572 = 9333,   f(9333) = 932 + 332 = 9738, etc. See 41)

78572 = 364 + 544 + 544 + 814.

Page of Squares : First Upload June 2, 2008 ; Last Revised October 9, 2008
by Yoshio Mimura, Kobe, Japan

7858

78582 = 61748164, a zigzag square.

Page of Squares : First Upload June 2, 2008 ; Last Revised June 2, 2008
by Yoshio Mimura, Kobe, Japan

7860

78602 = 363 + 2893 + 3353.

Page of Squares : First Upload June 2, 2008 ; Last Revised June 2, 2008
by Yoshio Mimura, Kobe, Japan

7863

78632 = 123 + 2023 + 3773.

78632 = 61826769 appears in the decimal expressions of e:
  e = 2.71828•••61826769••• (from the 57937th digit)

Page of Squares : First Upload June 2, 2008 ; Last Revised November 4, 2008
by Yoshio Mimura, Kobe, Japan

7867

78672 = 63 + 1063 + 3933.

Page of Squares : First Upload June 2, 2008 ; Last Revised June 2, 2008
by Yoshio Mimura, Kobe, Japan

7868

938k + 1274k + 3430k + 6902k are squares for k = 1,2,3 (1122, 78682, 6099522).

Page of Squares : First Upload July 12, 2011 ; Last Revised July 12, 2011
by Yoshio Mimura, Kobe, Japan

7870

78702 = 35 + 175 + 205 + 265 + 345.

Page of Squares : First Upload June 2, 2008 ; Last Revised June 2, 2008
by Yoshio Mimura, Kobe, Japan

7872

78722 = 61968384, a zigzag square.

78722 = 61968384, and 6 * 1968 / 3 * 8 / 4 = 61 * 96 + 8 * 3 * 84 = 7872.

78722 = 163 + 1203 + 3923.

78725 = 30229114605778501632 :
32 + 02 + 222 + 92 + 12 + 12 + 42 + 62 + 02 + 52 + 72 + 782 + 52 + 02 + 12 + 62 + 322 = 7872.

Page of Squares : First Upload June 2, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

7875

78752± 2 are primes.

78754 = 3845937744140625,
and 32 + 82 + 42 + 592 + 32 + 72 + 72 + 442 + 12 + 402 + 62 + 252 = 7875.

Page of Squares : First Upload December 1, 2008 ; Last Revised January 11, 2014
by Yoshio Mimura, Kobe, Japan

7876

78762± 3 are primes.

78762 = 62031376, and 62 + 22 + 02 + 32 + 12 + 32 + 72 + 62 = 122.

Page of Squares : First Upload June 2, 2008 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

7878

78782 = 62062884, a square with even digits.

78782 = 1763 + 2733 + 3313.

Page of Squares : First Upload June 2, 2008 ; Last Revised June 2, 2008
by Yoshio Mimura, Kobe, Japan

7880

78802 = (22 + 4)(27862 + 4).

Page of Squares : First Upload January 11, 2014 ; Last Revised January 11, 2014
by Yoshio Mimura, Kobe, Japan

7882

78825 = 30421607071753462432 :
32 + 02 + 42 + 22 + 12 + 62 + 02 + 702 + 72 + 12 + 72 + 52 + 342 + 62 + 242 + 322 = 7882.

Page of Squares : First Upload December 8, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

7884

78842 = 62157456, and 6 + 2 + 1574 * 5 + 6 = 7884.

78842 = 1243 + 2343 + 3623.

Page of Squares : First Upload June 2, 2008 ; Last Revised June 2, 2008
by Yoshio Mimura, Kobe, Japan

7885

78852 = 13 + 423 + 3963.

Page of Squares : First Upload June 2, 2008 ; Last Revised June 2, 2008
by Yoshio Mimura, Kobe, Japan

7887

78874 = 3869433286343361,
and 32 + 82 + 692 + 42 + 32 + 322 + 82 + 62 + 32 + 432 + 32 + 62 + 12 = 7887,
and 32 + 82 + 692 + 432 + 322 + 82 + 62 + 32 + 42 + 32 + 32 + 62 + 12 = 7887.

Page of Squares : First Upload December 1, 2008 ; Last Revised December 1, 2008
by Yoshio Mimura, Kobe, Japan

7888

78885 = 30537572402534023168 :
32 + 02 + 52 + 32 + 72 + 572 + 22 + 42 + 02 + 22 + 532 + 402 + 22 + 32 + 12 + 62 + 82
= 32 + 02 + 532 + 72 + 572 + 22 + 42 + 02 + 22 + 52 + 32 + 402 + 22 + 32 + 12 + 62 + 82
= 32 + 02 + 52 + 32 + 72 + 572 + 22 + 402 + 22 + 532 + 42 + 02 + 22 + 32 + 12 + 62 + 82
= 32 + 02 + 532 + 72 + 572 + 22 + 402 + 22 + 52 + 32 + 42 + 02 + 22 + 32 + 12 + 62 + 82 = 7888.

Page of Squares : First Upload December 8, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

7889

The square root of 7889 is 88.820042...., and 88 = 82 + 22 + 02 + 02 + 42 + 22.

Page of Squares : First Upload June 2, 2008 ; Last Revised June 2, 2008
by Yoshio Mimura, Kobe, Japan

7890

78902 = 323 + 1153 + 3933.

Page of Squares : First Upload June 2, 2008 ; Last Revised June 2, 2008
by Yoshio Mimura, Kobe, Japan

7892

78922 = 1003 + 2953 + 3293.

Page of Squares : First Upload June 2, 2008 ; Last Revised June 2, 2008
by Yoshio Mimura, Kobe, Japan

7895

78955 = 30673311969262184375 :
32 + 02 + 62 + 72 + 32 + 32 + 12 + 12 + 92 + 62 + 92 + 22 + 62 + 22 + 12 + 82 + 432 + 752 = 7895.

Page of Squares : First Upload December 8, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

7896

78962 = (22 - 1)(482 - 1)(952 - 1).

78962 = 233 + 1743 + 3853 = 283 + 2463 + 3623 = 1683 + 2323 + 3563.

Komachi equations:
78962 = 9872 * 62 * 52 * 42 / 32 * 22 / 102 = 9872 * 62 / 52 * 42 / 32 / 22 * 102
 = 9872 / 62 / 52 * 42 * 32 * 22 * 102.

Page of Squares : First Upload June 2, 2008 ; Last Revised January 11, 2014
by Yoshio Mimura, Kobe, Japan