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5500 - 5599

5504

55042 = (32 + 7)(52 + 7)(62 + 7)(372 + 7).

Page of Squares : First Upload December 28, 2013 ; Last Revised December 28, 2013
by Yoshio Mimura, Kobe. Japan

5506

55062 = 30316036, and 302 + 312 + 602 + 32 + 62.

55062 = 30316036, 32 + 02 + 32 + 12 + 62 + 02 + 32 + 62 = 102.

Page of Squares : First Upload December 10, 2007 ; Last Revised November 25, 2008
by Yoshio Mimura, Kobe. Japan

5508

55082 = (12 + 8)(22 + 8)(142 + 8)(372 + 8) = (12 + 8)(22 + 8)(5302 + 8)
= (102 + 8)(142 + 8)(372 + 8) = (102 + 8)(5302 + 8) = (22 + 2)(42 + 2)(222 + 2)(242 + 2)
= (22 + 8)(32 + 8)(102 + 8)(372 + 8).

55082 = 723 + 1293 + 3033 = 903 + 2183 + 2683 = 2073 + 2163 + 2253
= 124 + 244 + 424 + 724 = 184 + 364 + 364 + 724 = 284 + 424 + 564 + 644.

Page of Squares : First Upload September 18, 2008 ; Last Revised December 28, 2013
by Yoshio Mimura, Kobe. Japan

5511

55112 = 1783 + 1853 + 2643.

Page of Squares : First Upload September 18, 2008 ; Last Revised September 18, 2008
by Yoshio Mimura, Kobe. Japan

5514

55142 = 30404196, a zigzag square.

The square root of 74.2563...., and 74 = 22 + 52 + 62 + 32.

Page of Squares : First Upload December 10, 2007 ; Last Revised December 10, 2007
by Yoshio Mimura, Kobe. Japan

5516

46k + 170k + 202k + 258k are squares for k = 1,2,3 (262, 3722, 55162).

Page of Squares : First Upload June 21, 2011 ; Last Revised June 21, 2011
by Yoshio Mimura, Kobe. Japan

5517

55172 = 573 + 2283 + 2643.

Page of Squares : First Upload September 18, 2008 ; Last Revised September 18, 2008
by Yoshio Mimura, Kobe. Japan

5518

55182 = 733 + 1043 + 3073.

Page of Squares : First Upload September 18, 2008 ; Last Revised September 18, 2008
by Yoshio Mimura, Kobe. Japan

5520

55202 = (22 - 1)(32 - 1)(242 - 1)(472 - 1) = (52 - 1)(242 - 1)(472 - 1).

Page of Squares : First Upload December 28, 2013 ; Last Revised December 28, 2013
by Yoshio Mimura, Kobe. Japan

5522

55225 = 5134309107467193632 : 52 + 12 + 32 + 42 + 32 + 02 + 92 + 102 + 72 + 42 + 62 + 712 + 92 + 32 + 62 + 32 + 22 = 5522.

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

5525

55252 = (82 + 1)(182 + 1)(382 + 1).

Loop of length 56 by the function f(N) = ... + c2 + b2 + a2 where N = ... + 1002c + 100b + a:
5525 - 3650 - 3796 - 10585 - ... - 6817 - 4913 - 2570 - 5525
(Note f(5525) = 552 + 252 = 3650,   f(3650) = 362 + 502 = 3796, etc. See 41)

Page of Squares : First Upload October 9, 2008 ; Last Revised November 2, 2013
by Yoshio Mimura, Kobe. Japan

5526

55262 = 30536676, 305 * 3 * 6 + 6 * 7 - 6 = 305 * 3 * 6 - 6 + 7 * 6 = 5526.

Page of Squares : First Upload December 10, 2007 ; Last Revised December 10, 2007
by Yoshio Mimura, Kobe. Japan

5529

55292 = 63 + 1303 + 3053.

55292 = 30569841, a sqaure with different digits.

55292 = 30569841, 3 * 0 + 56 * 98 + 41 = 5529.

55292± 2 are primes.

55294 = 934515178765281, and 92 + 32 + 42 + 52 + 152 + 12 + 72 + 82 + 72 + 652 + 282 + 12 = 5529.

Page of Squares : First Upload December 10, 2007 ; Last Revised December 29, 2013
by Yoshio Mimura, Kobe. Japan

5530

55302 = (22 + 6)(82 + 6)(2092 + 6).

55302 = 542 x 543 + 544 x 545 + 546 x 547 + 548 x 549 + ... + 698 x 699.

Page of Squares : First Upload December 10, 2007 ; Last Revised December 28, 2013
by Yoshio Mimura, Kobe. Japan

5531

55312 = 813 + 2243 + 2663.

Page of Squares : First Upload September 18, 2008 ; Last Revised September 18, 2008
by Yoshio Mimura, Kobe. Japan

5535

55352 = 30636225, 306 * 3 * 6 + 2 + 25 = 306 * 3 * 6 + 22 + 5 = 5535.

Page of Squares : First Upload December 10, 2007 ; Last Revised December 10, 2007
by Yoshio Mimura, Kobe. Japan

5536

55362 = 243 + 643 + 3123 = 973 + 2263 + 2633.

55362 = 30647296, a zigzag square.

Page of Squares : First Upload December 10, 2007 ; Last Revised September 18, 2008
by Yoshio Mimura, Kobe. Japan

5540

95540955409 = 3090972.

Page of Squares : First Upload December 10, 2007 ; Last Revised December 10, 2007
by Yoshio Mimura, Kobe. Japan

5541

The square root of 5541 is 74.437...., and 74 = 42 + 32 + 72.

Page of Squares : First Upload December 10, 2007 ; Last Revised December 10, 2007
by Yoshio Mimura, Kobe. Japan

5542

55422 = 34 + 94 + 574 + 674.

55422 = 30713764, 32 + 02 + 72 + 12 + 32 + 72 + 62 + 42 = 132.

Page of Squares : First Upload December 10, 2007 ; Last Revised September 18, 2008
by Yoshio Mimura, Kobe. Japan

5544

55442 = (102 - 1)(132 - 1)(432 - 1) = (32 - 1)(102 - 1)(1972 - 1).

852 + 5544 = 1132, 852 - 5544 = 412.

The integral triangle of sides 10549, 12322, 22185 has square area 55442.

Page of Squares : First Upload August 2, 2011 ; Last Revised December 28, 2013
by Yoshio Mimura, Kobe. Japan

5545

55452 = 373 + 2213 + 2713.

Page of Squares : First Upload September 18, 2008 ; Last Revised September 18, 2008
by Yoshio Mimura, Kobe. Japan

5549

5549 = (12 + 22 + 32 + ... + 8052) / (12 + 22 + 32 + ... + 452).

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

5550

55502 = (12 + 9)(42 + 9)(182 + 9)(192 + 9) = (12 + 9)(42 + 9)(3512 + 9).

Page of Squares : First Upload December 28, 2013 ; Last Revised December 28, 2013
by Yoshio Mimura, Kobe. Japan

5552

55522 = 343 + 1483 + 3023.

Page of Squares : First Upload September 18, 2008 ; Last Revised September 18, 2008
by Yoshio Mimura, Kobe. Japan

5554

55542± 3 are primes.

1 / 5554 = 0.00018005041411595, 182 + 0052 + 042 + 12 + 412 + 12 + 592 + 52 = 5554,
1 / 5554 = 0.00018005041411595, 182 + 0052 + 0412 + 42 + 12 + 12 + 592 + 52 = 5554.

Page of Squares : First Upload December 10, 2007 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe. Japan

5556

55562 = 823 + 2363 + 2583.

55562 = 30869136, 30 + 8 * 6 + 913 * 6 = 5556.

Page of Squares : First Upload December 10, 2007 ; Last Revised September 18, 2008
by Yoshio Mimura, Kobe. Japan

5559

55592 = 473 + 1093 + 3093.

Page of Squares : First Upload September 18, 2008 ; Last Revised September 18, 2008
by Yoshio Mimura, Kobe. Japan

5561

55612 = 283 + 813 + 3123.

The square root of 5561 is 74.57...., and 74 = 52 + 72.

Page of Squares : First Upload December 10, 2007 ; Last Revised September 18, 2008
by Yoshio Mimura, Kobe. Japan

5562

55622 = 394 + 394 + 574 + 634.

The square root of 5562 is 74.57...., and 74 = 52 + 72.

Page of Squares : First Upload December 10, 2007 ; Last Revised September 18, 2008
by Yoshio Mimura, Kobe. Japan

5563

55632 = 75 + 85 + 115 + 235 + 305.

Page of Squares : First Upload September 18, 2008 ; Last Revised September 18, 2008
by Yoshio Mimura, Kobe. Japan

5564

55642 = 30958096, a zigzag.

Page of Squares : First Upload December 10, 2007 ; Last Revised December 10, 2007
by Yoshio Mimura, Kobe. Japan

5567

55672 = 344 + 364 + 484 + 694.

55675 = 5346949797563452607 : 52 + 32 + 42 + 62 + 92 + 492 + 72 + 92 + 72 + 52 + 62 + 32 + 452 + 262 + 02 + 72 = 5567.

Page of Squares : First Upload September 18, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe. Japan

5568

55682 = 1443 + 2243 + 2563.

Page of Squares : First Upload September 18, 2008 ; Last Revised September 18, 2008
by Yoshio Mimura, Kobe. Japan

5569

1 / 5569 = 0.00017956, and 17956 = 1342.

Page of Squares : First Upload December 10, 2007 ; Last Revised December 10, 2007
by Yoshio Mimura, Kobe. Japan

5570

The square root of 5570 is 74.63243...., and 74 = 62 + 32 + 22 + 42 + 32.

55702 = 4552 + 4572 + 4592 + 4612 + 4632 + ... + 6532.

Page of Squares : First Upload December 10, 2007 ; Last Revised December 10, 2007
by Yoshio Mimura, Kobe. Japan

5571

55712 = 1283 + 1773 + 2863.

55715 = 5366186869952956851 : 52 + 362 + 62 + 182 + 62 + 82 + 62 + 92 + 92 + 52 + 292 + 52 + 62 + 82 + 512 = 5571.

Page of Squares : First Upload September 18, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe. Japan

5576

55762 = 2003 + 2243 + 2283.

Page of Squares : First Upload September 18, 2008 ; Last Revised September 18, 2008
by Yoshio Mimura, Kobe. Japan

5579

55792 = 703 + 1883 + 2893.

Page of Squares : First Upload September 18, 2008 ; Last Revised September 18, 2008
by Yoshio Mimura, Kobe. Japan

5582

55822 = 31158724, 32 + 12 + 12 + 52 + 82 + 72 + 22 + 42 = 132.

Page of Squares : First Upload December 10, 2007 ; Last Revised December 10, 2007
by Yoshio Mimura, Kobe. Japan

5583

55832 = 24 + 534 + 544 + 624.

1 / 5583 = 0.00017911517105, 172 + 92 + 112 + 52 + 12 + 712 + 02 + 52 = 5583,
1 / 5583 = 0.00017911517105, 172 + 92 + 112 + 52 + 12 + 712 + 052 = 5583.

55835 = 5424230535860368143 : 542 + 22 + 42 + 232 + 02 + 52 + 32 + 52 + 82 + 62 + 02 + 32 + 62 + 82 + 12 + 432 = 5583.

Page of Squares : First Upload December 10, 2007 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe. Japan

5584

55842 = 1523 + 1883 + 2763.

Page of Squares : First Upload September 18, 2008 ; Last Revised September 18, 2008
by Yoshio Mimura, Kobe. Japan

5585

55853 = 174208576625, and 12 + 72 + 42 + 202 + 82 + 52 + 72 + 662 + 252 = 5585.

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

5586

55862 = 31203396, 31 * 20 * 3 / 3 * 9 + 6 = 31 * 20 / 3 * 3 * 9 + 6 = 5586.

The integral triangle of sides 3770, 17833, 19551 has square area 55862.

Komachi equations:
55862 = 982 * 762 * 52 / 42 * 32 * 22 / 102 = 982 * 762 / 52 / 42 * 32 / 22 * 102.

Page of Squares : First Upload December 10, 2007 ; Last Revised October 14, 2011
by Yoshio Mimura, Kobe. Japan

5587

55872 = 37 + 57 + 77 + 77 + 107 + 117.

Page of Squares : First Upload September 18, 2008 ; Last Revised September 18, 2008
by Yoshio Mimura, Kobe. Japan

5588

55882 = 1323 + 2223 + 2623.

The square root of 5588 is 74.75...., and 74 = 72 + 52.

Page of Squares : First Upload December 10, 2007 ; Last Revised September 18, 2008
by Yoshio Mimura, Kobe. Japan

5589

The square root of 5589 is 74.75...., and 74 = 72 + 52.

Page of Squares : First Upload December 10, 2007 ; Last Revised December 10, 2007
by Yoshio Mimura, Kobe. Japan

5595

55952 = 31304025, 32 + 12 + 32 + 02 + 42 + 02 + 22 + 52 = 82.

Page of Squares : First Upload December 10, 2007 ; Last Revised December 10, 2007
by Yoshio Mimura, Kobe. Japan

5597

The square root of 5597 is 74.813...., and 74 = 82 + 12 + 32.

Page of Squares : First Upload December 10, 2007 ; Last Revised December 10, 2007
by Yoshio Mimura, Kobe. Japan

5598

55984 = 982045424460816, and 92 + 82 + 202 + 452 + 42 + 242 + 462 + 02 + 82 + 162 = 5598.

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