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8700 - 8799

8700

87002 = 403 + 783 + 4223 = 863 + 1603 + 4143.

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

8706

87062± 5 are primes.

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

8708

87082 = 75829264, a zigzag square.

2282k + 3010k + 3626k + 6958k are squares for k = 1,2,3 (1262, 87082, 6509162).

Page of Squares : First Upload August 4, 2008 ; Last Revised July 15, 2011
by Yoshio Mimura, Kobe, Japan

8712

87122 = 1303 + 1403 + 4143 = 664 + 664 + 664 + 664.

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

8713

87134 = 5763295082144161,
and 52 + 762 + 32 + 22 + 92 + 502 + 82 + 22 + 142 + 42 + 12 + 62 + 12 = 8713.

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

8714

87142 = 75933796, a square with odd digits except the last digit 6.

Page of Squares : First Upload August 24, 2013 ; Last Revised August 24, 2013
by Yoshio Mimura, Kobe, Japan

8715

87152 = 43 + 3213 + 3503.

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

8716

87162 = 75968656, and 7 + 59 - 6 + 8656 = 75 - 9 - 6 + 8656 = 8716.

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

8717

87172 = 75986089, and 72 + 52 + 92 + 82 + 62 + 02 + 82 + 92 = 202.

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

8721

87212 = (372 + 8)(2352 + 8) = (72 + 8)(312 + 8)(372 + 8).

87212 = 1533 + 1543 + 1553 + 1563 + 1573 + ... + 1703.

Page of Squares : First Upload November 25, 2008 ; Last Revised January 11, 2014
by Yoshio Mimura, Kobe, Japan

8722

87222 = 74 + 494 + 774 + 774.

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

8723

130k + 1937k + 4264k + 7358k are squares for k = 1,2,3 (1172, 87232, 6950972).

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

8725

87255 = 50562341569814453125 :
52 + 02 + 52 + 622 + 342 + 12 + 52 + 62 + 92 + 82 + 12 + 42 + 42 + 532 + 12 + 252 = 8725.

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

8726

87262± 3 are primes.

87262 = 76143076, and 72 + 62 + 12 + 42 + 32 + 02 + 72 + 62 = 142.

Page of Squares : First Upload August 4, 2008 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

8729

87292 = 76195441, and 72 + 62 + 12 + 92 + 52 + 42 + 42 + 12 = 152.

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

8730

87302 = (32 + 9)(312 + 9)(662 + 9).

The square root of 8730 is 93.43446...., and 93 = 42 + 32 + 42 + 42 + 62.

Page of Squares : First Upload August 4, 2008 ; Last Revised January 11, 2014
by Yoshio Mimura, Kobe, Japan

8731

87312 = 76230361, and 72 + 62 + 22 + 32 + 02 + 32 + 62 + 12 = 122.

Loop of length 14 by the function f(N) = ... + c2 + b2 + a2 where N = ... + 1002c + 100b + a:
8731 - 8530 - 8125 - 7186 - ... - 6964 - 8857 - 10993 - 8731
(Note f(8731) = 872 + 312 = 8530,   f(8530) = 852 + 302 = 8125, etc. See 1946)

Page of Squares : First Upload August 4, 2008 ; Last Revised October 9, 2008
by Yoshio Mimura, Kobe, Japan

8732

87322 = 164 + 164 + 464 + 924.

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

8733

87332 = (22 - 1)(50422 - 1).

Page of Squares : First Upload August 4, 2008 ; Last Revised January 11, 2014
by Yoshio Mimura, Kobe, Japan

8734

1 / 8734 = 0.00011449...., and 11449 = 1072.

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

8735

87352 = 93 + 2183 + 4043.

1 / 8735 = 0.00011448196, 112 + 442 + 812 + 92 + 62 = 8735.

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

8736

87362 = 76317696, and 7 * 6 + 3 * 1 * 7 * 69 * 6 = 8736.

87362 = (12 + 3)(32 + 3)(52 + 3)(72 + 3)(332 + 3) = (12 + 3)(32 + 3)(72 + 3)(92 + 3)(192 + 3)
= (132 - 1)(252 - 1)(272 - 1) = (22 - 1)(152 - 1)(3372 - 1).

1702 + 8736 = 1942, 1702 - 8736 = 1422.

Komachi equation: 87362 = 92 * 82 * 72 * 652 * 42 / 32 * 22 / 102.

Page of Squares : First Upload August 4, 2008 ; Last Revised January 11, 2014
by Yoshio Mimura, Kobe, Japan

8739

87392 = S2(476) + S2(494), where S2(n) = 12 + 22 + 32 + 42 + ... + n2.

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

8740

87405 = 50998471891062400000, and
502 + 92 + 92 + 82 + 42 + 72 + 182 + 92 + 102 + 622 + 402 + 02 + 02 + 02 + 02 = 8740.

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

8746

The square root of 8746 is 93.520051325...., and
93 = 52 + 22 + 02 + 02 + 52 + 12 + 32 + 22 + 52.

87462 = 76492516, and 76 / 4 * 92 * 5 + 1 * 6 = 76 / 4 * 92 * 5 * 1 + 6 = 8746.

87464 = 5851105004010256, and 582 + 512 + 102 + 502 + 02 + 42 + 02 + 102 + 22 + 52 + 62 = 8746.

87465 = 51173764365073698976, and
512 + 172 + 32 + 72 + 62 + 42 + 32 + 62 + 52 + 02 + 732 + 62 + 92 + 82 + 92 + 72 + 62 = 8746.

Page of Squares : First Upload August 4, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

8747

87474 = 5853781477180081, and
582 + 52 + 32 + 72 + 82 + 12 + 42 + 72 + 712 + 82 + 02 + 02 + 82 + 12 = 8747.

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

8748

87482 = 273 + 2163 + 4053.

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

8750

87502 = 76562500, and 7 * 6 * 5 / 6 / 2 * 500 = 7 / 6 * 5 * 6 / 2 * 500
= 7 * 6 * 5 / 6 * 250 + 0 = 7 / 6 * 5 * 6 * 250 + 0 = 8750.

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

8751

87512 = 1413 + 2993 + 3613.

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

8754

87542 = 76632516, and 72 + 62 + 62 + 32 + 22 + 52 + 12 + 62 = 142.

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

8755

1 / 8755 = 0.000114220445459, 12 + 12 + 42 + 22 + 202 + 442 + 542 + 592 = 8755.

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

8756

87562 = 2802 + 2812 + 2822 + 2832 + ... + 6312.

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

8757

87572 = 2243 + 2643 + 3613.

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

8758

87582 = 533 + 2563 + 3913.

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

8759

87595 = 51555218488115227799, and
512 + 52 + 52 + 52 + 22 + 12 + 82 + 482 + 82 + 12 + 12 + 522 + 272 + 72 + 92 + 92
= 512 + 52 + 52 + 522 + 12 + 82 + 482 + 82 + 12 + 12 + 52 + 22 + 272 + 72 + 92 + 92 = 8759.

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

8760

Komachi equation: 87602 = 92 * 8762 / 542 * 32 * 22 * 102.

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

8761

8761 is the 6th prime for which the Lendre Symbol (a / 8761) = 1 for a = 1, 2,..., 16.

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

8763

87632 = 13 + 3263 + 3483.

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

8764

87642 = 76807696, a zigzag square.

87642± 3 are primes.

Page of Squares : First Upload August 4, 2008 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

8765

87655 = 51732039695574978125, and
512 + 72 + 322 + 02 + 392 + 62 + 92 + 552 + 72 + 42 + 92 + 72 + 82 + 122 + 52 = 8765.

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

8767

87672 = 76860289, and 76 + 8602 + 89 = 8767.

87674 = 5907504025163521, and
592 + 02 + 72 + 502 + 402 + 252 + 12 + 62 + 32 + 52 + 212 = 8767.

Page of Squares : First Upload August 4, 2008 ; Last Revised December 1, 2008
by Yoshio Mimura, Kobe, Japan

8768

87682 = 164 + 164 + 644 + 884.

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

8772

87722 = (112 + 8)(142 + 8)(542 + 8) = (22 + 8)(32 + 8)(112 + 8)(542 + 8).

87722 = 24 + 44 + 484 + 924.

87722 = 2111 x 2112 + 2113 x 2114 + 2115 x 2116 + 2117 x 2118 + ... + 2143 x 2144.

Page of Squares : First Upload August 4, 2008 ; Last Revised January 11, 2014
by Yoshio Mimura, Kobe, Japan

8773

87732 = 76965529, and 7 + 6 * 9 * 65 * 5 / 2 - 9 = 8773.

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

8774

87742 = 76983076, and 72 + 62 + 92 + 82 + 32 + 02 + 72 + 62 = 182.

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

8775

87752 = (62 + 9)(242 + 9)(542 + 9).

87752 = 3303 + 3453.

87755 = 52027819597177734375, and
522 + 02 + 272 + 82 + 192 + 592 + 72 + 12 + 72 + 72 + 72 + 342 + 32 + 72 + 52 = 8775.

Page of Squares : First Upload August 4, 2008 ; Last Revised January 11, 2014
by Yoshio Mimura, Kobe, Japan

8776

87762 = 763 + 1883 + 4123.

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

8778

87782 = 1443 + 1453 + 1463 + 1473 + 1483 + ... + 1643.

87782 + 87792 + 878-2 + ... + 88442 = 88452 + 88462 + 88472 + ... + 89102.

The integral triangle of sides 6521, 28633, 32760 (or 18513, 43339, 61610) has square area 87782.

Page of Squares : First Upload November 25, 2008 ; Last Revised October 21, 2011
by Yoshio Mimura, Kobe, Japan

8779

87794 = 5939914532447281, and
592 + 392 + 92 + 12 + 42 + 532 + 22 + 42 + 42 + 72 + 282 + 12 = 8779.

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

8783

87832 = 124 + 574 + 644 + 844.

87835 = 52265416277126304143, and
522 + 22 + 62 + 52 + 42 + 12 + 622 + 72 + 72 + 122 + 62 + 32 + 02 + 42 + 12 + 432 = 522 + 22 + 62 + 52 + 412 + 62 + 22 + 72 + 72 + 12 + 22 + 632 + 02 + 42 + 142 + 32 = 8783.

Page of Squares : First Upload August 4, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

8785

87855 = 52324950860626740625, and
52 + 22 + 322 + 492 + 52 + 02 + 82 + 62 + 02 + 62 + 22 + 672 + 42 + 02 + 62 + 252 = 8785.

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

8786

87862 = 77193796, a square with odd digits except the last digit 6.

Page of Squares : First Upload August 24, 2013 ; Last Revised August 24, 2013
by Yoshio Mimura, Kobe, Japan

8788

87882 = 3383 + 3383.

87885 = 52414354446428935168, and
522 + 42 + 142 + 32 + 52 + 42 + 42 + 42 + 642 + 22 + 82 + 92 + 352 + 162 + 82
= 522 + 42 + 142 + 352 + 42 + 42 + 42 + 642 + 22 + 82 + 92 + 32 + 52 + 162 + 82 = 8788.

Page of Squares : First Upload August 4, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

8791

1 / 8791 = 0.0001137527016266, 12 + 132 + 72 + 522 + 702 + 162 + 262 + 62 = 8791.

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

8792

87924 = 5975176214941696, and
592 + 72 + 512 + 72 + 62 + 22 + 12 + 492 + 42 + 12 + 62 + 92 + 62 = 8792.

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

8793

87932 = 1993 + 3053 + 3453.

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

8794

87945 = 52593528234706616224, and
52 + 252 + 92 + 352 + 282 + 232 + 42 + 702 + 62 + 62 + 12 + 62 + 222 + 42 = 8794.

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

8799

1 / 8799 = 0.000113649278, 12 + 132 + 62 + 42 + 922 + 72 + 82 = 8799.

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