## 8700

8700^{2} = 40^{3} + 78^{3} + 422^{3} = 86^{3} + 160^{3} + 414^{3}.

by Yoshio Mimura, Kobe, Japan

## 8706

8706^{2}± 5 are primes.

by Yoshio Mimura, Kobe, Japan

## 8708

8708^{2} = 75829264, a zigzag square.

2282^{k} + 3010^{k} + 3626^{k} + 6958^{k} are squares for k = 1,2,3 (126^{2}, 8708^{2}, 650916^{2}).

by Yoshio Mimura, Kobe, Japan

## 8712

8712^{2} = 130^{3} + 140^{3} + 414^{3} = 66^{4} + 66^{4} + 66^{4} + 66^{4}.

by Yoshio Mimura, Kobe, Japan

## 8713

8713^{4} = 5763295082144161,

and 5^{2} + 76^{2} + 3^{2} + 2^{2} + 9^{2} + 50^{2} + 8^{2} + 2^{2} + 14^{2} + 4^{2} + 1^{2} + 6^{2} + 1^{2} = 8713.

by Yoshio Mimura, Kobe, Japan

## 8714

8714^{2} = 75933796, a square with odd digits except the last digit 6.

by Yoshio Mimura, Kobe, Japan

## 8715

8715^{2} = 4^{3} + 321^{3} + 350^{3}.

by Yoshio Mimura, Kobe, Japan

## 8716

8716^{2} = 75968656, and 7 + 59 - 6 + 8656 = 75 - 9 - 6 + 8656 = 8716.

by Yoshio Mimura, Kobe, Japan

## 8717

8717^{2} = 75986089, and 7^{2} + 5^{2} + 9^{2} + 8^{2} + 6^{2} + 0^{2} + 8^{2} + 9^{2} = 20^{2}.

by Yoshio Mimura, Kobe, Japan

## 8721

8721^{2} = (37^{2} + 8)(235^{2} + 8) = (7^{2} + 8)(31^{2} + 8)(37^{2} + 8).

8721^{2} = 153^{3} + 154^{3} + 155^{3} + 156^{3} + 157^{3} + ... + 170^{3}.

by Yoshio Mimura, Kobe, Japan

## 8722

8722^{2} = 7^{4} + 49^{4} + 77^{4} + 77^{4}.

by Yoshio Mimura, Kobe, Japan

## 8723

130^{k} + 1937^{k} + 4264^{k} + 7358^{k} are squares for k = 1,2,3 (117^{2}, 8723^{2}, 695097^{2}).

by Yoshio Mimura, Kobe, Japan

## 8725

8725^{5} = 50562341569814453125 :

5^{2} + 0^{2} + 5^{2} + 62^{2} + 34^{2} + 1^{2} + 5^{2} + 6^{2} + 9^{2} + 8^{2} + 1^{2} + 4^{2} + 4^{2} + 53^{2} + 1^{2} + 25^{2} = 8725.

by Yoshio Mimura, Kobe, Japan

## 8726

8726^{2}± 3 are primes.

8726^{2} = 76143076, and 7^{2} + 6^{2} + 1^{2} + 4^{2} + 3^{2} + 0^{2} + 7^{2} + 6^{2} = 14^{2}.

by Yoshio Mimura, Kobe, Japan

## 8729

8729^{2} = 76195441, and 7^{2} + 6^{2} + 1^{2} + 9^{2} + 5^{2} + 4^{2} + 4^{2} + 1^{2} = 15^{2}.

by Yoshio Mimura, Kobe, Japan

## 8730

8730^{2} = (3^{2} + 9)(31^{2} + 9)(66^{2} + 9).

The square root of 8730 is 93.43446...., and 93 = 4^{2} + 3^{2} + 4^{2} + 4^{2} + 6^{2}.

by Yoshio Mimura, Kobe, Japan

## 8731

8731^{2} = 76230361, and 7^{2} + 6^{2} + 2^{2} + 3^{2} + 0^{2} + 3^{2} + 6^{2} + 1^{2} = 12^{2}.

Loop of length 14 by the function f(N) = ... + c^{2} + b^{2} + a^{2} where N = ... + 100^{2}c + 100b + a:

8731 - 8530 - 8125 - 7186 - ... - 6964 - 8857 - 10993 - 8731

(Note f(8731) = 87^{2} + 31^{2} = 8530, f(8530) = 85^{2} + 30^{2} = 8125, etc. See 1946)

by Yoshio Mimura, Kobe, Japan

## 8732

8732^{2} = 16^{4} + 16^{4} + 46^{4} + 92^{4}.

by Yoshio Mimura, Kobe, Japan

## 8733

8733^{2} = (2^{2} - 1)(5042^{2} - 1).

by Yoshio Mimura, Kobe, Japan

## 8734

1 / 8734 = 0.00011449...., and 11449 = 107^{2}.

by Yoshio Mimura, Kobe, Japan

## 8735

8735^{2} = 9^{3} + 218^{3} + 404^{3}.

1 / 8735 = 0.00011448196, 11^{2} + 44^{2} + 81^{2} + 9^{2} + 6^{2} = 8735.

by Yoshio Mimura, Kobe, Japan

## 8736

8736^{2} = 76317696, and 7 * 6 + 3 * 1 * 7 * 69 * 6 = 8736.

8736^{2} = (1^{2} + 3)(3^{2} + 3)(5^{2} + 3)(7^{2} + 3)(33^{2} + 3) = (1^{2} + 3)(3^{2} + 3)(7^{2} + 3)(9^{2} + 3)(19^{2} + 3)

= (13^{2} - 1)(25^{2} - 1)(27^{2} - 1) = (2^{2} - 1)(15^{2} - 1)(337^{2} - 1).

170^{2} + 8736 = 194^{2}, 170^{2} - 8736 = 142^{2}.

Komachi equation: 8736^{2} = 9^{2} * 8^{2} * 7^{2} * 65^{2} * 4^{2} / 3^{2} * 2^{2} / 10^{2}.

by Yoshio Mimura, Kobe, Japan

## 8739

8739^{2} = S_{2}(476) + S_{2}(494), where S_{2}(n) = 1^{2} + 2^{2} + 3^{2} + 4^{2} + ... + n^{2}.

by Yoshio Mimura, Kobe, Japan

## 8740

8740^{5} = 50998471891062400000, and

50^{2} + 9^{2} + 9^{2} + 8^{2} + 4^{2} + 7^{2} + 18^{2} + 9^{2} + 10^{2} + 62^{2} + 40^{2} + 0^{2} + 0^{2} + 0^{2} + 0^{2} = 8740.

by Yoshio Mimura, Kobe, Japan

## 8746

The square root of 8746 is 93.520051325...., and

93 = 5^{2} + 2^{2} + 0^{2} + 0^{2} + 5^{2} + 1^{2} + 3^{2} + 2^{2} + 5^{2}.

8746^{2} = 76492516, and 76 / 4 * 92 * 5 + 1 * 6 = 76 / 4 * 92 * 5 * 1 + 6 = 8746.

8746^{4} = 5851105004010256, and 58^{2} + 51^{2} + 10^{2} + 50^{2} + 0^{2} + 4^{2} + 0^{2} + 10^{2} + 2^{2} + 5^{2} + 6^{2} = 8746.

8746^{5} = 51173764365073698976, and

51^{2} + 17^{2} + 3^{2} + 7^{2} + 6^{2} + 4^{2} + 3^{2} + 6^{2} + 5^{2} + 0^{2} + 73^{2} + 6^{2} + 9^{2} + 8^{2} + 9^{2} + 7^{2} + 6^{2} = 8746.

by Yoshio Mimura, Kobe, Japan

## 8747

8747^{4} = 5853781477180081, and

58^{2} + 5^{2} + 3^{2} + 7^{2} + 8^{2} + 1^{2} + 4^{2} + 7^{2} + 71^{2} + 8^{2} + 0^{2} + 0^{2} + 8^{2} + 1^{2} = 8747.

by Yoshio Mimura, Kobe, Japan

## 8748

8748^{2} = 27^{3} + 216^{3} + 405^{3}.

by Yoshio Mimura, Kobe, Japan

## 8750

8750^{2} = 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.

by Yoshio Mimura, Kobe, Japan

## 8751

8751^{2} = 141^{3} + 299^{3} + 361^{3}.

by Yoshio Mimura, Kobe, Japan

## 8754

8754^{2} = 76632516, and 7^{2} + 6^{2} + 6^{2} + 3^{2} + 2^{2} + 5^{2} + 1^{2} + 6^{2} = 14^{2}.

by Yoshio Mimura, Kobe, Japan

## 8755

1 / 8755 = 0.000114220445459, 1^{2} + 1^{2} + 4^{2} + 2^{2} + 20^{2} + 44^{2} + 54^{2} + 59^{2} = 8755.

by Yoshio Mimura, Kobe, Japan

## 8756

8756^{2} = 280^{2} + 281^{2} + 282^{2} + 283^{2} + ... + 631^{2}.

by Yoshio Mimura, Kobe, Japan

## 8757

8757^{2} = 224^{3} + 264^{3} + 361^{3}.

by Yoshio Mimura, Kobe, Japan

## 8758

8758^{2} = 53^{3} + 256^{3} + 391^{3}.

by Yoshio Mimura, Kobe, Japan

## 8759

8759^{5} = 51555218488115227799, and

51^{2} + 5^{2} + 5^{2} + 5^{2} + 2^{2} + 1^{2} + 8^{2} + 48^{2} + 8^{2} + 1^{2} + 1^{2} + 52^{2} + 27^{2} + 7^{2} + 9^{2} + 9^{2}

= 51^{2} + 5^{2} + 5^{2} + 52^{2} + 1^{2} + 8^{2} + 48^{2} + 8^{2} + 1^{2} + 1^{2} + 5^{2} + 2^{2} + 27^{2} + 7^{2} + 9^{2} + 9^{2} = 8759.

by Yoshio Mimura, Kobe, Japan

## 8760

Komachi equation: 8760^{2} = 9^{2} * 876^{2} / 54^{2} * 3^{2} * 2^{2} * 10^{2}.

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, 2008by Yoshio Mimura, Kobe, Japan

## 8763

8763^{2} = 1^{3} + 326^{3} + 348^{3}.

by Yoshio Mimura, Kobe, Japan

## 8764

8764^{2} = 76807696, a zigzag square.

8764^{2}± 3 are primes.

by Yoshio Mimura, Kobe, Japan

## 8765

8765^{5} = 51732039695574978125, and

51^{2} + 7^{2} + 32^{2} + 0^{2} + 39^{2} + 6^{2} + 9^{2} + 55^{2} + 7^{2} + 4^{2} + 9^{2} + 7^{2} + 8^{2} + 12^{2} + 5^{2} = 8765.

by Yoshio Mimura, Kobe, Japan

## 8767

8767^{2} = 76860289, and 76 + 8602 + 89 = 8767.

8767^{4} = 5907504025163521, and

59^{2} + 0^{2} + 7^{2} + 50^{2} + 40^{2} + 25^{2} + 1^{2} + 6^{2} + 3^{2} + 5^{2} + 21^{2} = 8767.

by Yoshio Mimura, Kobe, Japan

## 8768

8768^{2} = 16^{4} + 16^{4} + 64^{4} + 88^{4}.

by Yoshio Mimura, Kobe, Japan

## 8772

8772^{2} = (11^{2} + 8)(14^{2} + 8)(54^{2} + 8) = (2^{2} + 8)(3^{2} + 8)(11^{2} + 8)(54^{2} + 8).

8772^{2} = 2^{4} + 4^{4} + 48^{4} + 92^{4}.

8772^{2} = 2111 x 2112 + 2113 x 2114 + 2115 x 2116 + 2117 x 2118 + ... + 2143 x 2144.

by Yoshio Mimura, Kobe, Japan

## 8773

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

by Yoshio Mimura, Kobe, Japan

## 8774

8774^{2} = 76983076, and 7^{2} + 6^{2} + 9^{2} + 8^{2} + 3^{2} + 0^{2} + 7^{2} + 6^{2} = 18^{2}.

by Yoshio Mimura, Kobe, Japan

## 8775

8775^{2} = (6^{2} + 9)(24^{2} + 9)(54^{2} + 9).

8775^{2} = 330^{3} + 345^{3}.

8775^{5} = 52027819597177734375, and

52^{2} + 0^{2} + 27^{2} + 8^{2} + 19^{2} + 59^{2} + 7^{2} + 1^{2} + 7^{2} + 7^{2} + 7^{2} + 34^{2} + 3^{2} + 7^{2} + 5^{2} = 8775.

by Yoshio Mimura, Kobe, Japan

## 8776

8776^{2} = 76^{3} + 188^{3} + 412^{3}.

by Yoshio Mimura, Kobe, Japan

## 8778

8778^{2} = 144^{3} + 145^{3} + 146^{3} + 147^{3} + 148^{3} + ... + 164^{3}.

8778^{2} + 8779^{2} + 878-^{2} + ... + 8844^{2} = 8845^{2} + 8846^{2} + 8847^{2} + ... + 8910^{2}.

The integral triangle of sides 6521, 28633, 32760 (or 18513, 43339, 61610) has square area 8778^{2}.

by Yoshio Mimura, Kobe, Japan

## 8779

8779^{4} = 5939914532447281, and

59^{2} + 39^{2} + 9^{2} + 1^{2} + 4^{2} + 53^{2} + 2^{2} + 4^{2} + 4^{2} + 7^{2} + 28^{2} + 1^{2} = 8779.

by Yoshio Mimura, Kobe, Japan

## 8783

8783^{2} = 12^{4} + 57^{4} + 64^{4} + 84^{4}.

8783^{5} = 52265416277126304143, and

52^{2} + 2^{2} + 6^{2} + 5^{2} + 4^{2} + 1^{2} + 62^{2} + 7^{2} + 7^{2} + 12^{2} + 6^{2} + 3^{2} + 0^{2} + 4^{2} + 1^{2} + 43^{2} = 52^{2} + 2^{2} + 6^{2} + 5^{2} + 41^{2} + 6^{2} + 2^{2} + 7^{2} + 7^{2} + 1^{2} + 2^{2} + 63^{2} + 0^{2} + 4^{2} + 14^{2} + 3^{2} = 8783.

by Yoshio Mimura, Kobe, Japan

## 8785

8785^{5} = 52324950860626740625, and

5^{2} + 2^{2} + 32^{2} + 49^{2} + 5^{2} + 0^{2} + 8^{2} + 6^{2} + 0^{2} + 6^{2} + 2^{2} + 67^{2} + 4^{2} + 0^{2} + 6^{2} + 25^{2} = 8785.

by Yoshio Mimura, Kobe, Japan

## 8786

8786^{2} = 77193796, a square with odd digits except the last digit 6.

by Yoshio Mimura, Kobe, Japan

## 8788

8788^{2} = 338^{3} + 338^{3}.

8788^{5} = 52414354446428935168, and

52^{2} + 4^{2} + 14^{2} + 3^{2} + 5^{2} + 4^{2} + 4^{2} + 4^{2} + 64^{2} + 2^{2} + 8^{2} + 9^{2} + 35^{2} + 16^{2} + 8^{2}

= 52^{2} + 4^{2} + 14^{2} + 35^{2} + 4^{2} + 4^{2} + 4^{2} + 64^{2} + 2^{2} + 8^{2} + 9^{2} + 3^{2} + 5^{2} + 16^{2} + 8^{2} = 8788.

by Yoshio Mimura, Kobe, Japan

## 8791

1 / 8791 = 0.0001137527016266, 1^{2} + 13^{2} + 7^{2} + 52^{2} + 70^{2} + 16^{2} + 26^{2} + 6^{2} = 8791.

by Yoshio Mimura, Kobe, Japan

## 8792

8792^{4} = 5975176214941696, and

59^{2} + 7^{2} + 51^{2} + 7^{2} + 6^{2} + 2^{2} + 1^{2} + 49^{2} + 4^{2} + 1^{2} + 6^{2} + 9^{2} + 6^{2} = 8792.

by Yoshio Mimura, Kobe, Japan

## 8793

8793^{2} = 199^{3} + 305^{3} + 345^{3}.

by Yoshio Mimura, Kobe, Japan

## 8794

8794^{5} = 52593528234706616224, and

5^{2} + 25^{2} + 9^{2} + 35^{2} + 28^{2} + 23^{2} + 4^{2} + 70^{2} + 6^{2} + 6^{2} + 1^{2} + 6^{2} + 22^{2} + 4^{2} = 8794.

by Yoshio Mimura, Kobe, Japan

## 8799

1 / 8799 = 0.000113649278, 1^{2} + 13^{2} + 6^{2} + 4^{2} + 92^{2} + 7^{2} + 8^{2} = 8799.

by Yoshio Mimura, Kobe, Japan