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6600 - 6699

6600

66002 = 1603 + 1763 + 3243.

3553k + 4554k + 5742k + 6600k are squares for k = 1,2,3 (1432, 104832, 7849272).

Page of Squares : First Upload October 2, 2008 ; Last Revised July 1, 2011
by Yoshio Mimura, Kobe, Japan

6601

The square root of 6601 is 81.2465...., and 81 = 22 + 42 + 62 + 52.

66012 = S2(21) + S2(507).

Page of Squares : First Upload March 3, 2008 ; Last Revised March 3, 2008
by Yoshio Mimura, Kobe, Japan

6603

1 / 6603 = 0.0001514463, 12 + 512 + 42 + 42 + 632 = 6603.

Page of Squares : First Upload March 3, 2008 ; Last Revised March 3, 2008
by Yoshio Mimura, Kobe, Japan

6605

The square root of 6605 is 81.271151...., and 81 = 22 + 72 + 12 + 12 + 52 + 12.

Page of Squares : First Upload March 3, 2008 ; Last Revised March 3, 2008
by Yoshio Mimura, Kobe, Japan

6606

66064 = 1904382918663696,
and 12 + 92 + 02 + 42 + 382 + 292 + 12 + 82 + 62 + 632 + 62 + 92 + 62 = 6606.

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

6607

66072 = 34 + 64 + 644 + 724.

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

6611

66114 = 1910155083713041, and 192 + 102 + 12 + 552 + 02 + 82 + 372 + 12 + 32 + 02 + 412 = 6611.

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

6612

66122 = 43718544, and 42 + 32 + 72 + 12 + 82 + 52 + 42 + 42 = 142.

969k + 5016k + 5092k + 6612k are squares for k = 1,2,3 (1332, 97852, 7404112).

Page of Squares : First Upload March 3, 2008 ; Last Revised July 1, 2011
by Yoshio Mimura, Kobe, Japan

6615

66152 = (102 + 5)(202 + 5)(322 + 5).

66152 = 43758225, and 42 + 32 + 72 + 52 + 82 + 22 + 22 + 52 = 142.

Komachi equations:
66152 = 92 * 82 * 72 / 62 * 52 / 42 * 32 * 212 = 92 / 82 * 72 * 62 * 52 * 42 / 32 * 212
 = 982 / 72 * 62 * 52 / 42 * 32 * 212.

66155 = 12666284617821384375 :
12 + 22 + 62 + 662 + 22 + 82 + 42 + 62 + 12 + 72 + 82 + 212 + 382 + 42 + 32 + 72 + 52
= 12 + 22 + 662 + 62 + 22 + 82 + 42 + 62 + 12 + 72 + 82 + 212 + 382 + 42 + 32 + 72 + 52 = 6615.

Page of Squares : First Upload March 3, 2008 ; Last Revised January 11, 2014
by Yoshio Mimura, Kobe, Japan

6616

66162 = 363 + 483 + 3523 = 1283 + 2563 + 2923 = 1353 + 2583 + 2893.

66162 = 1993 + 95 + 127.

Page of Squares : First Upload October 2, 2008 ; Last Revised November 2, 2010
by Yoshio Mimura, Kobe, Japan

6618

66182 = 253 + 1263 + 3473.

66182 = 43797924, 4 * 3 * 79 * 7 - 9 / 2 * 4 = 6618.

Page of Squares : First Upload March 3, 2008 ; Last Revised October 2, 2008
by Yoshio Mimura, Kobe, Japan

6621

66212± 2 are primes.

66215 = 12723832385873557101 :
122 + 72 + 22 + 382 + 32 + 22 + 382 + 582 + 72 + 32 + 52 + 52 + 72 + 12 + 02 + 12 = 6621.

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

6622

5698k + 6622k + 8338k + 10318k are squares for k = 1,2,3 (1762, 158842, 14674882).

66225 = 12733443982644401632 :
12 + 272 + 32 + 342 + 432 + 92 + 82 + 22 + 62 + 42 + 42 + 402 + 12 + 62 + 322
= 122 + 72 + 32 + 32 + 42 + 432 + 92 + 82 + 22 + 642 + 42 + 42 + 02 + 162 + 32 + 22 = 6622.

Page of Squares : First Upload December 8, 2008 ; Last Revised July 1, 2011
by Yoshio Mimura, Kobe, Japan

6623

66232 = 493 + 2183 + 3223.

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

6624

66242 = 1923 + 2643 + 2643.

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

6625

66252 = 253 + 1003 + 3503.

66252 = 43890625, a square with different digits.

Page of Squares : First Upload March 3, 2008 ; Last Revised October 2, 2008
by Yoshio Mimura, Kobe, Japan

6629

The square root of 6629 is 81.418...., and 81 = 42 + 12 + 82.

Page of Squares : First Upload March 3, 2008 ; Last Revised March 3, 2008
by Yoshio Mimura, Kobe, Japan

6630

1482k + 6630k + 15418k + 19734k are squares for k = 1,2,3 (2082, 259482, 34124482).

66302 = (22 + 9)(292 + 9)(632 + 9) = (22 + 9)(42 + 9)(52 + 9)(632 + 9).

66302 = 1443 + 1453 + 1463 + 1473 + 1483 + ... + 1563.

The integral triangle of sides 10201, 18735, 28186 has square area 66302.

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

6633

66332 = 43996689, 43 - 99 + 6689 = 6633.

Page of Squares : First Upload March 3, 2008 ; Last Revised March 3, 2008
by Yoshio Mimura, Kobe, Japan

6638

66385 = 12888021157371923168 :
122 + 82 + 82 + 82 + 02 + 22 + 12 + 152 + 732 + 72 + 192 + 22 + 32 + 162 + 82 = 6638.

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

6641

66412 = 44102881, 4 * 410 / 2 * 8 + 81 = 6641.

Page of Squares : First Upload March 3, 2008 ; Last Revised March 3, 2008
by Yoshio Mimura, Kobe, Japan

6642

66422 = (12 + 2)(22 + 2)(222 + 2)(712 + 2) = (12 + 2)(22 + 2)(42 + 2)(52 + 2)(712 + 2)
= (22 + 5)(62 + 5)(72 + 5)(472 + 5) = (42 + 2)(222 + 2)(712 + 2).

66422 = 1443 + 2373 + 3033 = 94 + 234 + 474 + 794 = 94 + 274 + 274 + 814.

66422 = 44116164, a square with just 3 kinds of digits.

Page of Squares : First Upload March 3, 2008 ; Last Revised January 11, 2014
by Yoshio Mimura, Kobe, Japan

6643

66435 = 12936633131256641443 :
12 + 22 + 92 + 32 + 62 + 62 + 332 + 12 + 32 + 122 + 562 + 62 + 42 + 142 + 432
= 122 + 92 + 32 + 62 + 62 + 332 + 12 + 32 + 12 + 22 + 562 + 62 + 42 + 142 + 432
= 12 + 22 + 92 + 362 + 62 + 32 + 32 + 132 + 122 + 562 + 62 + 412 + 42 + 42 + 32
= 122 + 92 + 362 + 62 + 32 + 32 + 132 + 12 + 22 + 562 + 62 + 412 + 42 + 42 + 32 = 6643.

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

6644

66442 = (22 + 7)(122 + 7)(1632 + 7).

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

6645

66455 = 12956118943555153125 :
12 + 292 + 52 + 612 + 12 + 82 + 92 + 42 + 32 + 52 + 52 + 52 + 152 + 312 + 252 = 6645.

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

6646

66462 = 44169316, and 42 + 42 + 12 + 62 + 92 + 32 + 12 + 62 = 142.

Page of Squares : First Upload March 3, 2008 ; Last Revised March 3, 2008
by Yoshio Mimura, Kobe, Japan

6647

66472 = 174 + 344 + 684 + 684.

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

6651

66512± 2 are primes.

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

6654

66542 = 44275716, and 42 + 42 + 22 + 72 + 52 + 72 + 12 + 62 = 142.

Page of Squares : First Upload March 3, 2008 ; Last Revised March 3, 2008
by Yoshio Mimura, Kobe, Japan

6655

66552 = 683 + 2573 + 3003 = 225 + 335.

66552 = (374 + 375 + 376 + 377 + 378)2 + (379 + 380 + 381 + 382 + 383)2 + (384 + 385 + 386 + 387 + 388)2 + ... + (424 + 425 + 426 + 427 + 428)2.

Page of Squares : First Upload March 3, 2008 ; Last Revised October 2, 2008
by Yoshio Mimura, Kobe, Japan

6657

66572 = 43 + 2243 + 3213.

66575 = 13073527500060525057 :
12 + 302 + 72 + 352 + 272 + 52 + 02 + 02 + 02 + 602 + 52 + 22 + 52 + 02 + 52 + 72 = 6657.

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

6659

(66592 - 5) = (62 - 5)(82 - 5)(92 - 5)(182 - 5).

Page of Squares : First Upload March 3, 2008 ; Last Revised March 3, 2008
by Yoshio Mimura, Kobe, Japan

6660

66602 = 44355600, 44 * 3 * 55 - 600 = 6660.

Page of Squares : First Upload March 3, 2008 ; Last Revised March 3, 2008
by Yoshio Mimura, Kobe, Japan

6663

66632 = 1283 + 2733 + 2803.

66632 = 44395569, 42 + 42 + 32 + 92 + 52 + 52 + 62 + 92 = 172.

Page of Squares : First Upload March 3, 2008 ; Last Revised October 2, 2008
by Yoshio Mimura, Kobe, Japan

6664

66642 = 563 + 2663 + 2943 = 843 + 983 + 3503.

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

6665

66652 = 44422225, a square with just 3 kinds of digits.

Page of Squares : First Upload March 3, 2008 ; Last Revised March 3, 2008
by Yoshio Mimura, Kobe, Japan

6666

66662 = 44435556, and
4 - 4 + 4 * 3 * 555 + 6 = 4 * 4 / 4 * 3 * 555 + 6 = 4 / 4 * 4 * 3 * 555 + 6
= 444 * 3 * 5 + 5 - 5 + 6 = 444 * 3 * 5 + 5 / 5 * 6 = 444 * 3 * 5 - 5 + 5 + 6
= 444 * 3 * 5 * 5 / 5 + 6 = 444 * 3 * 5 / 5 * 5 + 6 = 444 * 3 / 5 * 5 * 5 + 6 = 6666.

66665 = 13162141234436220576 : 12 + 32 + 12 + 62 + 212 + 42 + 12 + 22 + 342 + 42 + 362 + 22 + 202 + 572 + 62 = 12 + 32 + 162 + 22 + 142 + 12 + 232 + 442 + 32 + 62 + 22 + 202 + 572 + 62 = 12 + 32 + 162 + 22 + 142 + 12 + 232 + 42 + 432 + 62 + 222 + 02 + 572 + 62 = 6666.

Page of Squares : First Upload March 3, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

6667

66672 = 44448889, a square with just 3 kinds of digits which form a non-decreasing sequence.

Page of Squares : First Upload March 3, 2008 ; Last Revised March 3, 2008
by Yoshio Mimura, Kobe, Japan

6668

66682 = 44462224, a square with just 3 kinds of even digits.

Page of Squares : First Upload March 3, 2008 ; Last Revised March 3, 2008
by Yoshio Mimura, Kobe, Japan

6669

The square root of 6669 is 81.663...., and 81 = 62 + 62 + 32.

Page of Squares : First Upload March 3, 2008 ; Last Revised March 3, 2008
by Yoshio Mimura, Kobe, Japan

6672

66722 = 1003 + 2363 + 3123 = 324 + 484 + 644 + 684.

66722 = 44515584, and 445 * 15 - 5 + 8 / 4 = 6672.

Page of Squares : First Upload March 3, 2008 ; Last Revised October 2, 2008
by Yoshio Mimura, Kobe, Japan

6674

66742± 3 are primes.

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

6675

66752 = 44555625, and
445 * 5 * 5 * 6 / 2 / 5 = 445 * 5 / 5 * 6 / 2 * 5 = 445 / 5 * 5 * 6 / 2 * 5 = 6675.

Page of Squares : First Upload March 3, 2008 ; Last Revised March 3, 2008
by Yoshio Mimura, Kobe, Japan

6678

66782 = 25 + 45 + 215 + 265 + 315.

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

6681

66812 = 283 + 2813 + 2823 = 743 + 2173 + 3243.

2550k + 2652k + 6681k + 11526k are squares for k = 1,2,3 (1532, 138212, 13655252).

Page of Squares : First Upload October 2, 2008 ; Last Revised July 1, 2011
by Yoshio Mimura, Kobe, Japan

6682

5330k + 6682k + 7514k + 13598k are squares for k = 1,2,3 (1822, 177322, 18407482).

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

6686

66862 = 833 + 1693 + 3403.

66865 = 13360781487984798176 :
12 + 32 + 32 + 602 + 72 + 82 + 12 + 42 + 82 + 72 + 92 + 82 + 472 + 92 + 82 + 172 + 62
= 132 + 32 + 602 + 72 + 82 + 12 + 482 + 72 + 92 + 82 + 42 + 72 + 92 + 82 + 12 + 72 + 62 = 6686.

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

6687

66872 = 103 + 2013 + 3323 = 64 + 514 + 664 + 664.

66872 = 44715969, 4 - 4 + 7 * 159 * 6 + 9 = 4 / 4 * 7 * 159 * 6 + 9 = 6687.

Page of Squares : First Upload March 3, 2008 ; Last Revised October 2, 2008
by Yoshio Mimura, Kobe, Japan

6688

66884 = 2000714214670336,
and 202 + 02 + 02 + 712 + 42 + 22 + 12 + 42 + 62 + 72 + 02 + 332 + 62 = 6688.

66882 = 44729344, and
4 + 4 + 72 * 93 - 4 * 4 = 4 - 4 + 72 * 93 - 4 - 4 = 4 / 4 * 72 * 93 - 4 - 4 = 6688.

66882 = 30 + 32 + 34 + 36 + 37 + 38 + 39 + 310 + 313 + 316.

Page of Squares : First Upload March 3, 2008 ; Last Revised August 30, 2011
by Yoshio Mimura, Kobe, Japan

6690

6690k + 103026k + 142497k + 195348k are squares for k = 1,2,3 (6692, 2629172, 1069670792).

66904 = 2003108487210000,
and 202 + 02 + 312 + 02 + 82 + 42 + 82 + 722 + 12 + 02 + 02 + 02 + 02 = 6690.

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

6692

1 / 6692 = 0.000149432157, 12 + 492 + 42 + 322 + 12 + 572 = 6692.

Page of Squares : First Upload March 3, 2008 ; Last Revised March 3, 2008
by Yoshio Mimura, Kobe, Japan

6693

66932 = 44796249, and 4 + 4 + 7 * 962 - 49 = 6693.

Page of Squares : First Upload March 3, 2008 ; Last Revised March 3, 2008
by Yoshio Mimura, Kobe, Japan

6695

66952 = 44823025, and 448 / 2 * 30 - 25 = 6695.

Page of Squares : First Upload March 3, 2008 ; Last Revised March 3, 2008
by Yoshio Mimura, Kobe, Japan

6696

66962 = 783 + 3543.

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

6697

66973 = 300359170873, and 302 + 02 + 32 + 52 + 92 + 172 + 02 + 82 + 732 = 6697.

66975 = 13471051445052413257 :
12 + 32 + 42 + 72 + 102 + 512 + 42 + 42 + 52 + 02 + 52 + 242 + 12 + 32 + 22 + 572
= 12 + 342 + 72 + 102 + 52 + 12 + 442 + 52 + 02 + 522 + 42 + 12 + 32 + 252 + 72
= 12 + 342 + 72 + 12 + 02 + 512 + 42 + 452 + 02 + 52 + 242 + 132 + 22 + 52 + 72 = 6697.

Page of Squares : First Upload December 1, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

6698

The square root of 6698 is 81.841...., and 81 = 82 + 42 + 12.

Page of Squares : First Upload March 3, 2008 ; Last Revised March 3, 2008
by Yoshio Mimura, Kobe, Japan

6699

66992 = S2(26) + S2(512).

Page of Squares : First Upload March 3, 2008 ; Last Revised March 3, 2008
by Yoshio Mimura, Kobe, Japan