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8800 - 8899

8800

88002 = 165 + 245 + 245 + 365.

Page of Squares : First Upload August 10, 2008 ; Last Revised August 10, 2008
by Yoshio Mimura, Kobe, Japan

8801

88012 = 523 + 823 + 4253.

88012 = 77457601, and 72 + 72 + 42 + 52 + 72 + 62 + 02 + 12 = 152.

Page of Squares : First Upload August 10, 2008 ; Last Revised August 10, 2008
by Yoshio Mimura, Kobe, Japan

8803

88032 = 1693 + 3103 + 3503.

The square root of 8803 is 93.8243...., and 93 = 82 + 22 + 42 + 32.

Page of Squares : First Upload August 10, 2008 ; Last Revised August 10, 2008
by Yoshio Mimura, Kobe, Japan

8806

578k + 2754k + 6358k + 8806k are squares for k = 1,2,3 (1362, 112202, 9802882).

88064 = 6013325662644496, and
and 602 + 132 + 322 + 562 + 62 + 262 + 42 + 42 + 42 + 92 + 62 = 8806.

88065 = 52953345785247431776, and
522 + 92 + 52 + 332 + 42 + 52 + 72 + 82 + 522 + 42 + 72 + 432 + 12 + 72 + 72 + 62 = 8806.

Page of Squares : First Upload December 1, 2008 ; Last Revised July 15, 2011
by Yoshio Mimura, Kobe, Japan

8807

88072 = 77563249, and 7 * 7 * 5 * 6 * 3 * 2 - 4 - 9 = 8807.

1 / 8807 = 0.00011354604292040, 112 + 352 + 42 + 602 + 422 + 92 + 202 + 402 = 8807.

Page of Squares : First Upload August 10, 2008 ; Last Revised August 10, 2008
by Yoshio Mimura, Kobe, Japan

8810

88102 = 1963 + 2633 + 3733.

Page of Squares : First Upload August 10, 2008 ; Last Revised August 10, 2008
by Yoshio Mimura, Kobe, Japan

8812

88125 = 53133991554755832832 :
52 + 32 + 12 + 32 + 392 + 92 + 12 + 52 + 52 + 472 + 552 + 82 + 32 + 282 + 322
= 52 + 32 + 12 + 32 + 392 + 92 + 12 + 552 + 472 + 52 + 52 + 82 + 32 + 282 + 322 = 8812.

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

8813

88132 = (12 + 6)(33312 + 6).

88132 = 77668969, a square every digit of which is greater than 5.

Page of Squares : First Upload September 7, 2013 ; Last Revised January 11, 2014
by Yoshio Mimura, Kobe, Japan

8814

88145 = 53194316243764441824 :
52 + 312 + 92 + 432 + 12 + 62 + 22 + 42 + 372 + 642 + 42 + 42 + 182 + 22 + 42
= 532 + 12 + 92 + 42 + 32 + 12 + 62 + 22 + 42 + 372 + 642 + 42 + 42 + 182 + 22 + 42 = 8814.

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

8815

88152 = 77704225, and 72 + 72 + 72 + 02 + 42 + 22 + 22 + 52 = 142.

Page of Squares : First Upload August 10, 2008 ; Last Revised August 10, 2008
by Yoshio Mimura, Kobe, Japan

8820

88202 = (12 + 5)(32 + 5)(52 + 5)(102 + 5)(172 + 5) = (32 + 5)(52 + 5)(172 + 5)(252 + 5)
= (33 + 8)(103 + 8)(133 + 8).

Komachi equation: 88202 = 982 / 72 / 62 * 542 / 32 * 2102.

Page of Squares : First Upload November 16, 2010 ; Last Revised January 11, 2014
by Yoshio Mimura, Kobe, Japan

8822

1 / 8822 = 0.00011335298118, 112 + 32 + 352 + 292 + 812 + 12 + 82 = 8822.

88225 = 53436163156603617632 :
52 + 32 + 42 + 32 + 62 + 12 + 62 + 312 + 52 + 62 + 602 + 32 + 62 + 12 + 72 + 632 + 22 = 8822.

Page of Squares : First Upload August 10, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

8823

88232 = 174 + 364 + 684 + 864 = 364 + 474 + 584 + 884.

Page of Squares : First Upload August 10, 2008 ; Last Revised August 10, 2008
by Yoshio Mimura, Kobe, Japan

8824

88242 = 77862976, and 77 * 8 + 6 * 2 * 9 * 76 = 8824.

Page of Squares : First Upload August 10, 2008 ; Last Revised August 10, 2008
by Yoshio Mimura, Kobe, Japan

8826

88262 = 513 + 1003 + 4253.

Page of Squares : First Upload August 10, 2008 ; Last Revised August 10, 2008
by Yoshio Mimura, Kobe, Japan

8827

1 / 8827 = 0.00011328877, 112 + 322 + 82 + 872 + 72 = 8827.

Page of Squares : First Upload August 10, 2008 ; Last Revised August 10, 2008
by Yoshio Mimura, Kobe, Japan

8828

88282 = 1003 + 2193 + 4053 = 1723 + 2143 + 3983.

Page of Squares : First Upload August 10, 2008 ; Last Revised August 10, 2008
by Yoshio Mimura, Kobe, Japan

8830

88305 = 53678888912464300000 :
52 + 32 + 672 + 82 + 82 + 82 + 82 + 92 + 12 + 22 + 462 + 432 + 02 + 02 + 02 + 02 + 02 = 8830.

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

8833

8833 = 882 + 332.

88332 = 24 + 184 + 424 + 934 = 164 + 374 + 684 + 864.

88335 = 53770138135912459393 :
52 + 372 + 702 + 12 + 32 + 82 + 12 + 32 + 52 + 92 + 122 + 452 + 92 + 32 + 92 + 32 = 8833.

Page of Squares : First Upload August 10, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

8834

88342 = 78039556, and 72 + 82 + 02 + 32 + 92 + 52 + 52 + 62 = 172.

88345 = 53800582104181819424 :
52 + 32 + 802 + 02 + 52 + 82 + 22 + 102 + 412 + 82 + 12 + 82 + 192 + 42 + 22 + 42 = 8834.

Page of Squares : First Upload August 10, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

8835

88352 = 513 + 3373 + 3413.

S2(8885) = S2(5596) + S2(8073), where S2(n) = 12 + 22 + 32 + 42 + ... + n2.

Page of Squares : First Upload August 10, 2008 ; Last Revised August 10, 2008
by Yoshio Mimura, Kobe, Japan

8836

The square of 94.

Page of Squares : First Upload August 10, 2008 ; Last Revised August 10, 2008
by Yoshio Mimura, Kobe, Japan

8840

88402 = (12 + 4)(22 + 4)(32 + 4)(92 + 4)(422 + 4) = (12 + 4)(32 + 4)(262 + 4)(422 + 4)
= (12 + 4)(422 + 4)(942 + 4) = (12 + 4)(92 + 4)(102 + 4)(422 + 4)
= (22 + 4)(32 + 4)(92 + 4)(942 + 4) = (32 + 4)(262 + 4)(942 + 4)
= (32 + 4)(62 + 4)(92 + 4)(422 + 4) = (32 + 4)(92 + 4)(102 + 4)(262 + 4)
= (92 + 4)(102 + 4)(942 + 4).

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

8841

88412 = 93 + 3283 + 3503.

Page of Squares : First Upload August 10, 2008 ; Last Revised August 10, 2008
by Yoshio Mimura, Kobe, Japan

8844

88442 = (22 + 8)(272 + 8)(942 + 8).

88445 = 54105780901490740224 :
52 + 42 + 12 + 02 + 52 + 72 + 802 + 92 + 02 + 12 + 42 + 92 + 02 + 72 + 402 + 222 + 42 = 8844.

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

8845

88455 = 54136376795812028125 :
52 + 42 + 12 + 32 + 62 + 372 + 62 + 72 + 92 + 52 + 812 + 202 + 22 + 82 + 122 + 52 = 8845.

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

8846

88462 = 1183 + 1453 + 4193.

88462 = 78251716, a zigzag square.

88462 = 78251716, and 7 * 82 + 517 * 16 = 8846.

Page of Squares : First Upload August 10, 2008 ; Last Revised August 10, 2008
by Yoshio Mimura, Kobe, Japan

8847

88472 = 2493 + 3023 + 3283
= 24 + 24 + 214 + 944 = 124 + 244 + 424 + 934 = 184 + 364 + 364 + 934.

Page of Squares : First Upload August 10, 2008 ; Last Revised August 10, 2008
by Yoshio Mimura, Kobe, Japan

8848

88482 = 2313 + 2923 + 3453.

88485 = 54228247535149907968 :
52 + 42 + 22 + 22 + 82 + 22 + 42 + 72 + 52 + 32 + 52 + 142 + 92 + 902 + 72 + 92 + 62 + 82 = 8848.

Page of Squares : First Upload August 10, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

8850

88502 = (122 + 6)(172 + 6)(422 + 6) = (22 + 6)(32 + 6)(172 + 6)(422 + 6).

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

8851

88512 = 78340201, a zigzag square.

Page of Squares : First Upload August 10, 2008 ; Last Revised August 10, 2008
by Yoshio Mimura, Kobe, Japan

8853

88532 = 78375609, a zigzag square.

273k + 8853k + 18213k + 27417k are squares for k = 1,2,3 (2342, 340862, 52291982).

Page of Squares : First Upload August 10, 2008 ; Last Revised July 15, 2011
by Yoshio Mimura, Kobe, Japan

8854

88545 = 54412363190235229024 :
542 + 412 + 232 + 62 + 312 + 92 + 02 + 22 + 352 + 22 + 292 + 02 + 242 = 8854.

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

8855

88552 = 78411025, and 784 = 282, 11025 = 1052.

S2(8855) = S2(3317) + S2(8697), where S2(n) = 12 + 22 + 32 + 42 + ... + n2.

Page of Squares : First Upload August 10, 2008 ; Last Revised August 10, 2008
by Yoshio Mimura, Kobe, Japan

8856

88562 = 78428736, and 78 + 42 + 8736 = 8856.

Page of Squares : First Upload August 10, 2008 ; Last Revised August 10, 2008
by Yoshio Mimura, Kobe, Japan

8857

88572 = 78446449, 7 * 844 * 6 / 4 + 4 - 9 = 8857.

Loop of length 14 by the function f(N) = ... + c2 + b2 + a2 where N = ... + 1002c + 100b + a:
8857 - 10993 - 8731 - 8530 - ... - 4264 - 5860 - 6964 - 8857
(Note f(8857) = 882 + 572 = 10993,   f(10993) = 12 + 092 + 932 = 8731, etc. See 1946)

Page of Squares : First Upload August 10, 2008 ; Last Revised October 9, 2008
by Yoshio Mimura, Kobe, Japan

8861

88612 = 1943 + 2813 + 3663.

Page of Squares : First Upload August 10, 2008 ; Last Revised August 10, 2008
by Yoshio Mimura, Kobe, Japan

8864

88645 = 54720333668704845824 :
542 + 72 + 202 + 32 + 32 + 362 + 62 + 82 + 72 + 02 + 42 + 82 + 42 + 582 + 242 = 8864.

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

8865

88652 = 1333 + 1553 + 4173 = 1963 + 2183 + 3933.

88652 = (2087 + 2088 + 2089)2 + (2090 + 2091 + 2092)2 + (2093 + 2094 + 2095)2 + ... + (2090 + 2091 + 2092)2.

Page of Squares : First Upload August 10, 2008 ; Last Revised August 10, 2008
by Yoshio Mimura, Kobe, Japan

8866

88662± 3 are primes.

Page of Squares : First Upload August 10, 2008 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

8868

88682 = 933 + 1393 + 4223.

Page of Squares : First Upload August 10, 2008 ; Last Revised August 10, 2008
by Yoshio Mimura, Kobe, Japan

8870

88704 = 6190054593610000, and
62 + 12 + 92 + 02 + 02 + 52 + 42 + 52 + 932 + 62 + 12 + 02 + 02 + 02 + 02 = 8870.

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

8871

1 / 8871 = 0.0001127268628, 12 + 12 + 272 + 262 + 862 + 22 + 82 = 8871.

Page of Squares : First Upload August 10, 2008 ; Last Revised August 10, 2008
by Yoshio Mimura, Kobe, Japan

8872

88722 = 78712384, and 72 + 82 + 72 + 12 + 22 + 32 + 82 + 42 = 162.

Page of Squares : First Upload August 10, 2008 ; Last Revised August 10, 2008
by Yoshio Mimura, Kobe, Japan

8874

88742 = (32 + 9)(72 + 9)(122 + 9)(222 + 9) = (52 + 9)(122 + 9)(1232 + 9).

88742 = 78747876, a square pegged by 7.

Page of Squares : First Upload August 10, 2008 ; Last Revised January 11, 2014
by Yoshio Mimura, Kobe, Japan

8875

88752 = 1003 + 1003 + 4253 = 1503 + 2253 + 4003.

1 / 8875 = 0.00011267605633, 112 + 22 + 672 + 62 + 02 + 562 + 332 = 8875,
1 / 8875 = 0.00011267605633, 112 + 22 + 672 + 62 + 0562 + 332 = 8875.

Page of Squares : First Upload August 10, 2008 ; Last Revised August 10, 2008
by Yoshio Mimura, Kobe, Japan

8877

88772± 2 are primes.

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

8878

88782 = 1293 + 1463 + 4193.

Page of Squares : First Upload August 10, 2008 ; Last Revised August 10, 2008
by Yoshio Mimura, Kobe, Japan

8879

88792 = 78836641, and 7 + 8 + 8 + 36 * 6 * 41 = 8879 .

Page of Squares : First Upload August 10, 2008 ; Last Revised August 10, 2008
by Yoshio Mimura, Kobe, Japan

8880

88802 = 78854400 appears in the decimal expressions of π:
  π = 3.14159•••78854400••• (from the 31609th digit)
  (78854400 is the fifth 8-digit square in the expression of π.)

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

8881

The square root of 8881 is 94.239...., and 94 = 22 + 32 + 92.

88814 = 6220817780809921, and
62 + 22 + 22 + 02 + 82 + 12 + 72 + 72 + 82 + 02 + 82 + 02 + 92 + 922 + 12 = 8881.

Page of Squares : First Upload August 10, 2008 ; Last Revised December 1, 2008
by Yoshio Mimura, Kobe, Japan

8882

The square root of 8882 is 94.2443632...., and 94 = 22 + 42 + 42 + 32 + 62 + 32 + 22.

88822 = 78889924, and 7 + 8889 - 9 * 2 + 4 = 8882.

Page of Squares : First Upload August 10, 2008 ; Last Revised August 10, 2008
by Yoshio Mimura, Kobe, Japan

8884

88842 = 823 + 3243 + 3543.

Page of Squares : First Upload August 10, 2008 ; Last Revised August 10, 2008
by Yoshio Mimura, Kobe, Japan

8887

88872 = 78978769, a square every digit of which is greater than 5.

Page of Squares : First Upload September 7, 2013 ; Last Revised September 7, 2013
by Yoshio Mimura, Kobe, Japan

8888

88885 = 55465154831533703168 :
552 + 42 + 62 + 52 + 152 + 42 + 82 + 32 + 152 + 32 + 32 + 702 + 32 + 162 + 82 = 8888.

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

8889

88892 = 253 + 2163 + 4103.

Page of Squares : First Upload August 10, 2008 ; Last Revised August 10, 2008
by Yoshio Mimura, Kobe, Japan

8890

8890k + 12446k + 23368k + 100457k are squares for k = 1,2,3 (3812, 1042672, 320805812).

Page of Squares : First Upload July 15, 2011 ; Last Revised July 15, 2011
by Yoshio Mimura, Kobe, Japan

8891

88912 = 1853 + 2953 + 3613 = 2013 + 2673 + 3733.

88912 = 79049881, and 7904 + 988 - 1 = 8891.

Page of Squares : First Upload August 10, 2008 ; Last Revised August 10, 2008
by Yoshio Mimura, Kobe, Japan

8893

88934 = 6254508243531601, and
622 + 52 + 42 + 52 + 02 + 82 + 22 + 432 + 532 + 162 + 02 + 12 = 8893.

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

8898

The square root of 8898 is 94.329...., and 94 = 32 + 22 + 92.

Page of Squares : First Upload August 10, 2008 ; Last Revised August 10, 2008
by Yoshio Mimura, Kobe, Japan

8899

88992 = 15172 + 15192 + 15212 + 15232 + ... + 15812.

Page of Squares : First Upload August 10, 2008 ; Last Revised August 10, 2008
by Yoshio Mimura, Kobe, Japan