7601
76012 = 57775201, and 5 + 77 + 7520 - 1 = 7601.
Page of Squares : First Upload May 19, 2008 ; Last Revised May 19, 2008by Yoshio Mimura, Kobe, Japan
7602
76022 = (122 + 3)(6272 + 3).
Page of Squares : First Upload January 11, 2014 ; Last Revised January 11, 2014by Yoshio Mimura, Kobe, Japan
7604
76045 = 25422048385136129024 :
22 + 52 + 42 + 222 + 02 + 482 + 32 + 82 + 512 + 362 + 122 + 92 + 02 + 242 = 7604.
by Yoshio Mimura, Kobe, Japan
7605
76052 = 145 + 165 + 165 + 255 + 345.
76052 = (98 + 99 + 100 + ... + 136)2 + (137 + 138 + 139 + ... + 175)2.
Page of Squares : First Upload May 19, 2008 ; Last Revised May 19, 2008by Yoshio Mimura, Kobe, Japan
7610
Loop of length 56 by the function f(N) = ... + c2 + b2 + a2 where N = ... + 1002c + 100b + a:
7610 - 5876 - 9140 - 9881 - ... - 7528 - 6409 - 4177 - 7610
(Note f(7610) = 762 + 102 = 5876, f(5876) = 582 + 762 = 9140, etc. See 41)
76102 = 23 + 1733 + 3753.
Page of Squares : First Upload May 19, 2008 ; Last Revised October 9, 2008by Yoshio Mimura, Kobe, Japan
7611
76112 = 57927321, and 5 + 7927 - 321 = 7611.
Page of Squares : First Upload May 19, 2008 ; Last Revised May 19, 2008by Yoshio Mimura, Kobe, Japan
7613
76132 = 493 + 1283 + 3823.
Komachi equation: 76132 = 12 / 22 * 32 * 456782 / 92.
Page of Squares : First Upload May 19, 2008 ; Last Revised November 9, 2008by Yoshio Mimura, Kobe, Japan
7617
76172± 2 are primes.
76172 = 1003 + 1293 + 3803 = 2093 + 2823 + 2983.
Page of Squares : First Upload May 19, 2008 ; Last Revised January 11, 2014by Yoshio Mimura, Kobe, Japan
7618
76182 = 10052 + 10072 + 10092 + 10112 + ... + 11072.
1326k + 2730k + 5226k + 7618k are squares for k = 1,2,3 (1302, 97242, 7794282).
Page of Squares : First Upload May 19, 2008 ; Last Revised July 8, 2011by Yoshio Mimura, Kobe, Japan
7620
1065k + 3360k + 6180k + 7620k are squares for k = 1,2,3 (1352, 104252, 8471252).
Page of Squares : First Upload July 8, 2011 ; Last Revised July 8, 2011by Yoshio Mimura, Kobe, Japan
7621
76212 = 58079641, a square with different digits.
Page of Squares : First Upload May 19, 2008 ; Last Revised May 19, 2008by Yoshio Mimura, Kobe, Japan
7622
76222 = 1153 + 2123 + 3613.
Page of Squares : First Upload May 19, 2008 ; Last Revised May 19, 2008by Yoshio Mimura, Kobe, Japan
7623
76232 = 224 + 444 + 664 + 774 = 334 + 664 + 664 + 664.
Page of Squares : First Upload May 19, 2008 ; Last Revised May 19, 2008by Yoshio Mimura, Kobe, Japan
7625
76252 = 58140625, a zigzag square.
Page of Squares : First Upload May 19, 2008 ; Last Revised May 19, 2008by Yoshio Mimura, Kobe, Japan
7626
7626k + 9486k + 11656k + 18321k are squares for k = 1,2,3 (2172, 248932, 30050472).
76262 = 58155876, and 52 + 82 + 12 + 52 + 52 + 82 + 72 + 62 = 172.
Page of Squares : First Upload May 19, 2008 ; Last Revised July 8, 2011by Yoshio Mimura, Kobe, Japan
7627
76275 = 25808854660149906907 :
22 + 52 + 82 + 02 + 82 + 82 + 52 + 42 + 62 + 62 + 02 + 12 + 492 + 92 + 02 + 692 + 02 + 72 = 7627.
by Yoshio Mimura, Kobe, Japan
7629
1 / 7629 = 0.0001310787, 12 + 32 + 12 + 02 + 72 + 872 = 7629,
1 / 7629 = 0.0001310787, 12 + 32 + 12 + 072 + 872 = 7629.
76292 = 1023 + 1693 + 3743.
Page of Squares : First Upload May 19, 2008 ; Last Revised May 19, 2008by Yoshio Mimura, Kobe, Japan
7631
1 / 7631 = 0.000131044...., and 131044 = 3622.
76312 = 58232161,
and 52 + 82 + 22 + 32 + 22 + 12 + 62 + 12 = 122.
76315 = 25876603289764027151 :
22 + 52 + 82 + 72 + 662 + 02 + 322 + 82 + 92 + 72 + 62 + 402 + 22 + 72 + 152 + 12 = 7631.
by Yoshio Mimura, Kobe, Japan
7635
76352 = 58293225, and 5 + 82 * 93 - 2 / 2 + 5 = 7635.
Page of Squares : First Upload May 19, 2008 ; Last Revised May 19, 2008by Yoshio Mimura, Kobe, Japan
7636
76362 = 1763 + 2073 + 3533.
Page of Squares : First Upload May 19, 2008 ; Last Revised May 19, 2008by Yoshio Mimura, Kobe, Japan
7637
76374 = 3401662030365361,
and 32 + 402 + 12 + 62 + 62 + 22 + 02 + 302 + 362 + 52 + 32 + 612 = 7637.
by Yoshio Mimura, Kobe, Japan
7639
76395 = 26012527367615382199 :
22 + 62 + 02 + 12 + 22 + 52 + 22 + 732 + 62 + 72 + 62 + 152 + 382 + 22 + 192 + 92 = 7639.
by Yoshio Mimura, Kobe, Japan
7644
76442 = (12 + 3)(22 + 3)(62 + 3)(122 + 3)(192 + 3) = (122 + 3)(192 + 3)(332 + 3)
= (22 + 3)(52 + 3)(122 + 3)(452 + 3) = (22 + 3)(52 + 3)(62 + 3)(72 + 3)(122 + 3)
= (22 + 3)(72 + 3)(122 + 3)(332 + 3) = (32 + 3)(72 + 3)(3062 + 3)
= (52 + 3)(62 + 3)(122 + 3)(192 + 3) = (62 + 3)(332 + 3)(372 + 3).
76442 = 983 + 2103 + 3643.
Page of Squares : First Upload May 19, 2008 ; Last Revised January 11, 2014by Yoshio Mimura, Kobe, Japan
7646
76462 = 58461316, a zigzag square.
1 / 7646 = 0.00013078733, 12 + 32 + 02 + 72 + 872 + 32 + 32 = 7646,
1 / 7646 = 0.00013078733, 12 + 32 + 072 + 872 + 32 + 32 = 7646.
by Yoshio Mimura, Kobe, Japan
7647
76472 = 114 + 164 + 684 + 784 = 164 + 484 + 534 + 824 = 234 + 344 + 724 + 744.
Page of Squares : First Upload May 19, 2008 ; Last Revised May 19, 2008by Yoshio Mimura, Kobe, Japan
7648
76482 = 58461316, a zigzag square.
76482 = 44 + 444 + 684 + 764.
Page of Squares : First Upload May 19, 2008 ; Last Revised May 19, 2008by Yoshio Mimura, Kobe, Japan
7649
76492 = 1733 + 2833 + 3133 = 2013 + 2023 + 3483.
Page of Squares : First Upload May 19, 2008 ; Last Revised May 19, 2008by Yoshio Mimura, Kobe, Japan
7650
76502 = (12 + 9)(212 + 9)(1142 + 9) = (12 + 9)(32 + 9)(122 + 9)(462 + 9)
= (12 + 9)(32 + 9)(42 + 9)(1142 + 9) = (12 + 9)(42 + 9)(122 + 9)(392 + 9)
= (12 + 9)(42 + 9)(52 + 9)(62 + 9)(122 + 9) = (12 + 9)(62 + 9)(122 + 9)(292 + 9)
= (122 + 9)(212 + 9)(292 + 9) = (32 + 9)(392 + 9)(462 + 9) = (32 + 9)(42 + 9)(122 + 9)(292 + 9)
= (32 + 9)(52 + 9)(62 + 9)(462 + 9) = (42 + 9)(52 + 9)(122 + 9)(212 + 9)
= (42 + 9)(52 + 9)(62 + 9)(392 + 9) = (62 + 9)(292 + 9)(392 + 9).
76502 = 813 + 1313 + 3823.
Page of Squares : First Upload May 19, 2008 ; Last Revised January 11, 2014by Yoshio Mimura, Kobe, Japan
7653
76535 = 26251768551451673493 :
262 + 252 + 12 + 72 + 62 + 82 + 52 + 512 + 452 + 162 + 72 + 342 + 92 + 32 = 7653.
by Yoshio Mimura, Kobe, Japan
7654
76542 = 58583716, a zigzag square.
76542± 3 are primes.
(76542 - 2) = (32 - 2)(52 - 2)(72 - 2)(92 - 2)(102 - 2).
Page of Squares : First Upload May 19, 2008 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
7656
76562± 5 are primes.
76562 = 58614336, and 52 + 82 + 62 + 12 + 42 + 32 + 32 + 62 = 142.
76562 = 58614336, and 58 * 6 * 1 * 4 * 33 / 6 = 58 / 6 * 1 * 4 * 33 * 6 = 7656.
76565 = 26303262785423179776 :
22 + 62 + 32 + 02 + 32 + 22 + 62 + 272 + 82 + 52 + 42 + 232 + 172 + 92 + 72 + 762
= 22 + 62 + 32 + 02 + 322 + 62 + 22 + 72 + 82 + 52 + 42 + 22 + 32 + 12 + 792 + 72 + 72 + 62 = 7656.
by Yoshio Mimura, Kobe, Japan
7657
228k + 4104k + 5700k + 7657k are squares for k = 1,2,3 (1332, 103932, 8386032).
Page of Squares : First Upload July 8, 2011 ; Last Revised July 8, 2011by Yoshio Mimura, Kobe, Japan
7658
76582 = 873 + 2323 + 3573 = 1063 + 2973 + 3153.
Page of Squares : First Upload May 19, 2008 ; Last Revised May 19, 2008by Yoshio Mimura, Kobe, Japan
7659
76592 = (2 + 3 + 4 + ...+ 70)2 + (71 + 72 + 73 + ... + 139)2.
Page of Squares : First Upload May 19, 2008 ; Last Revised May 19, 2008by Yoshio Mimura, Kobe, Japan
7662
76625 = 26406493674109700832 :
22 + 62 + 42 + 02 + 62 + 492 + 32 + 62 + 72 + 42 + 12 + 02 + 92 + 702 + 02 + 82 + 32 + 22 = 7662.
by Yoshio Mimura, Kobe, Japan
7665
76652 = 213 + 2273 + 3613 = 763 + 2493 + 3503.
Page of Squares : First Upload May 19, 2008 ; Last Revised May 19, 2008by Yoshio Mimura, Kobe, Japan
7666
76665 = 26475494142541900576 :
262 + 42 + 72 + 52 + 492 + 42 + 142 + 252 + 42 + 192 + 02 + 02 + 572 + 62 = 7666.
by Yoshio Mimura, Kobe, Japan
7667
76672 = 1312 + 1332 + 1352 + 1372 + ... + 7072.
Page of Squares : First Upload May 19, 2008 ; Last Revised May 19, 2008by Yoshio Mimura, Kobe, Japan
7669
76692 = 58813561, and 52 + 82 + 82 + 12 + 32 + 52 + 62 + 12 = 152.
76692 = 353 + 1633 + 3793.
Page of Squares : First Upload May 19, 2008 ; Last Revised May 19, 2008by Yoshio Mimura, Kobe, Japan
7672
76725 = 26579265223026245632 :
22 + 62 + 572 + 92 + 22 + 62 + 52 + 22 + 22 + 32 + 02 + 22 + 62 + 22 + 42 + 562 + 322 = 7672.
by Yoshio Mimura, Kobe, Japan
7677
76775 = 26665989455023142157 :
22 + 62 + 62 + 652 + 92 + 82 + 92 + 42 + 552 + 02 + 22 + 32 + 12 + 42 + 22 + 12 + 52 + 72 = 7677.
by Yoshio Mimura, Kobe, Japan
7678
76784 = 3475301046435856,
and 32 + 472 + 52 + 32 + 02 + 102 + 42 + 62 + 432 + 582 + 52 + 62 = 7678.
by Yoshio Mimura, Kobe, Japan
7679
76792 = 58967041, a square with different digits.
76794 = 3477111924295681,
and 342 + 772 + 12 + 12 + 192 + 22 + 42 + 22 + 92 + 52 + 62 + 82 + 12 = 7679.
by Yoshio Mimura, Kobe, Japan
7680
1042 + 7680 = 1362, 1042 - 7680 = 562.
76802 = 643 + 1283 + 3843 = 723 + 1763 + 3763.
76802 = (13 + 23 + 33 + ... + 153)(163).
Page of Squares : First Upload May 19, 2008 ; Last Revised February 2, 2013by Yoshio Mimura, Kobe, Japan
7681
76812 = 58997761, and 5 - 8 + 99 * 77 + 61 = 7681.
Page of Squares : First Upload May 19, 2008 ; Last Revised May 19, 2008by Yoshio Mimura, Kobe, Japan
7684
76842 = 59043856, a zigzag square.
76842 = 59043856, and 52 + 92 + 02 + 42 + 32 + 82 + 52 + 62 = 162.
76842 = 504 + 604 + 604 + 724.
Loop of length 56 by the function f(N) = ... + c2 + b2 + a2 where N = ... + 1002c + 100b + a:
7684 - 12832 - 1809 - 405 - ... - 1066 - 4456 - 5072 - 7684
(Note f(7684) = 762 + 842 = 12832, f(12832) = 12 + 282 + 322 = 1809, etc. See 41)
by Yoshio Mimura, Kobe, Japan
7685
76855 = 26805218962660803125 :
22 + 62 + 82 + 02 + 52 + 22 + 182 + 92 + 62 + 22 + 62 + 62 + 02 + 802 + 32 + 12 + 252
= 22 + 62 + 802 + 52 + 22 + 182 + 92 + 62 + 22 + 62 + 62 + 02 + 82 + 02 + 32 + 12 + 252 = 7685.
by Yoshio Mimura, Kobe, Japan
7686
76862 = (12 + 5)(192 + 5)(1642 + 5).
Page of Squares : First Upload January 11, 2014 ; Last Revised January 11, 2014by Yoshio Mimura, Kobe, Japan
7687
76872 = 613 + 1913 + 3733.
76872 = 3553 + 275 + 37.
Page of Squares : First Upload May 19, 2008 ; Last Revised November 9, 2010by Yoshio Mimura, Kobe, Japan
7688
76882 = 224 + 384 + 384 + 864 = 624 + 624 + 624 + 624.
Page of Squares : First Upload May 19, 2008 ; Last Revised May 19, 2008by Yoshio Mimura, Kobe, Japan
7692
76922 = 783 + 2623 + 3443 = 1123 + 2463 + 3503.
Page of Squares : First Upload May 19, 2008 ; Last Revised May 19, 2008by Yoshio Mimura, Kobe, Japan
7694
76945 = 26962546670863488224 :
262 + 92 + 62 + 22 + 52 + 42 + 62 + 62 + 702 + 82 + 62 + 342 + 82 + 82 + 222 + 42 = 7694.
by Yoshio Mimura, Kobe, Japan
7695
Komachi equation: 76952 = 92 / 82 * 762 * 542 / 32 / 22 * 102.
Page of Squares : First Upload December 8, 2008 ; Last Revised November 9, 2010by Yoshio Mimura, Kobe, Japan
7696
76962 = (102 + 4)(122 + 4)(622 + 4) = (22 + 4)(32 + 4)(122 + 4)(622 + 4).
76962 = 484 + 604 + 804.
76962 = 30 + 34 + 37 + 310 + 311 + 313 + 315 + 316.
76965 = 26997608495344254976 :
262 + 92 + 92 + 72 + 62 + 02 + 82 + 492 + 52 + 342 + 42 + 252 + 492 + 72 + 62 = 7696.
by Yoshio Mimura, Kobe, Japan
7697
76972 = 59243809, a zigzag square.
The square root of 7697 is 87.7325...., and 87 = 72 + 32 + 22 + 52.
76972 = 14 + 164 + 464 + 864 = 284 + 344 + 564 + 834.
Page of Squares : First Upload May 19, 2008 ; Last Revised May 19, 2008by Yoshio Mimura, Kobe, Japan
7699
76992 = 59274601, a square with different digits.
Page of Squares : First Upload May 19, 2008 ; Last Revised May 19, 2008by Yoshio Mimura, Kobe, Japan