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1000 - 1099

6400

The square of 80.

64002 = 1603 + 1603 + 3203.

203 + 6400 = 1202, 203 - 6400 = 402.

Komachi equation: 64002 = 94 * 84 / 74 * 64 / 544 / 34 * 2104.

Page of Squares : First Upload February 18, 2008 ; Last Revised August 2, 2011
by Yoshio Mimura, Kobe, Japan

6402

64022 = 95 + 135 + 135 + 165 + 335.

6402k + 9570k + 9966k + 13266k are squares for k = 1,2,3 (1982, 201962, 21126602).

Page of Squares : First Upload September 29, 2008 ; Last Revised June 28, 2011
by Yoshio Mimura, Kobe, Japan

6404

1 / 6404 = 0.000156152404747, 12 + 52 + 62 + 152 + 242 + 042 + 742 + 72 = 6404,
1 / 6404 = 0.000156152404747, 152 + 62 + 12 + 52 + 242 + 042 + 742 + 72 = 6404.

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

6405

64052 = 41024025, 4 * 10 * 2 * 40 * 2 + 5 = 6405.

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

6408

64082 = (12 + 8)(42 + 8)(4362 + 8) = (82 + 8)(92 + 8)(802 + 8).

64082 = 64 + 424 + 664 + 664.

64082 = (26 + 27 + 28 + ... + 37)2 + (38 + 39 + 40 + ... + 49)2 + (50 + 51 + 52 + ... + 61)2 + ... + (206 + 207 + 208 + ... + 217)2.

Komachi equation: 64082 = 122 * 32 / 42 * 562 / 72 * 892.

Page of Squares : First Upload February 18, 2008 ; Last Revised January 11, 2014
by Yoshio Mimura, Kobe, Japan

6409

64092 = (22 + 9)(222 + 9)(802 + 9).

Loop of length 56 by the function f(N) = ... + c2 + b2 + a2 where N = ... + 1002c + 100b + a:
6409 - 4177 - 7610 - 5876 - ... - 13154 - 3878 - 7528 - 6409
(Note f(6409) = 642 + 092 = 4177,   f(4177) = 412 + 772 = 7610, etc. See 41)

Page of Squares : First Upload October 9, 2008 ; Last Revised January 11, 2014
by Yoshio Mimura, Kobe, Japan

6411

64112 = 413 + 1203 + 3403.

Page of Squares : First Upload September 29, 2008 ; Last Revised September 29, 2008
by Yoshio Mimura, Kobe, Japan

6412

S2(6412) = S2(4525) + S2(5550), where S2(n) = 12 + 22 + 32 + 42 + ... + n2.

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

6417

64172± 2 are primes.

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

6420

64202 = 233 + 523 + 3453.

64202 = 41216400, 41 - 21 + 6400 = 6420.

Page of Squares : First Upload February 18, 2008 ; Last Revised September 29, 2008
by Yoshio Mimura, Kobe, Japan

6421

64213 = 264732956461, and 22 + 642 + 72 + 32 + 22 + 92 + 52 + 62 + 462 + 12 = 6421.

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

6422

1 / 6422 = 0.00015571473061, 12 + 52 + 572 + 12 + 472 + 302 + 62 + 12 = 6422.

64222 = 41242084, and 42 + 12 + 22 + 42 + 22 + 02 + 82 + 42 = 112.

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

6423

64232 = 394 + 464 + 464 + 744.

Page of Squares : First Upload September 29, 2008 ; Last Revised September 29, 2008
by Yoshio Mimura, Kobe, Japan

6425

64252 = 103 + 603 + 3453 = 1353 + 1653 + 3253 = 54 + 204 + 204 + 804.

Page of Squares : First Upload September 29, 2008 ; Last Revised September 29, 2008
by Yoshio Mimura, Kobe, Japan

6426

The integral triangle of sides 19656, 137785, 157433 has square area 64262.

64265 = 10957301355204713376 :
12 + 02 + 92 + 52 + 72 + 302 + 132 + 52 + 522 + 02 + 472 + 132 + 32 + 72 + 62 = 6426.

Page of Squares : First Upload December 8, 2008 ; Last Revised October 18, 2011
by Yoshio Mimura, Kobe, Japan

6428

64282 = 41319184, a zigzag square.

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

6429

1 / 6429 = 0.00015554518587, 12 + 552 + 542 + 52 + 182 + 52 + 82 + 72 = 6429.

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

6430

64302 = 13012 + 13022 + 13032 + 13042 + 13052 + 13062 + ... + 13242.

1 / 6432 = 0.00015547263, 152 + 52 + 472 + 22 + 632 = 6432.

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

6432

64322 = 1243 + 1763 + 3243.

64324 = 1711528530149376,
and 12 + 712 + 12 + 52 + 22 + 82 + 52 + 302 + 142 + 92 + 32 + 72 + 62 = 6432.

Page of Squares : First Upload September 29, 2008 ; Last Revised December 1, 2008
by Yoshio Mimura, Kobe, Japan

6435

64352 = (42 - 1)(102 - 1)(122 - 1)(142 - 1).

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

6436

64362± 3 are primes.

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

6437

64372 = 41434969, and 42 + 12 + 42 + 32 + 42 + 92 + 62 + 92 = 162.

64375 = 11051406294871295957 :
12 + 102 + 52 + 142 + 02 + 62 + 22 + 92 + 482 + 72 + 12 + 22 + 92 + 592 + 52 + 72 = 6437.

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

6439

64392 = 41460721, and 4 * 1 * 460 * 7 / 2 - 1 = 6439.

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

6440

64402 = 143 + 2253 + 3113.

64405 = 11077183160422400000 :
12 + 102 + 772 + 182 + 32 + 12 + 62 + 02 + 42 + 22 + 22 + 42 + 02 + 02 + 02 + 02 + 02 = 6440.

Komachi equation: 64402 = 12 / 22 * 3452 * 62 * 72 * 82 / 92.

Page of Squares : First Upload September 29, 2008 ; Last Revised October 29, 2010
by Yoshio Mimura, Kobe, Japan

6441

64412± 2 are primes.

64412 = 253 + 2253 + 3113.

Page of Squares : First Upload September 29, 2008 ; Last Revised January 11, 2014
by Yoshio Mimura, Kobe, Japan

6442

64422 = 434 + 594 + 594 + 614.

64422 = 41499364, and 42 + 12 + 42 + 92 + 92 + 32 + 62 + 42 = 162.

Page of Squares : First Upload February 18, 2008 ; Last Revised September 29, 2008
by Yoshio Mimura, Kobe, Japan

6444

64442 = 703 + 783 + 3443.

Page of Squares : First Upload September 29, 2008 ; Last Revised September 29, 2008
by Yoshio Mimura, Kobe, Japan

6445

64452 = 41538025, 42 + 12 + 52 + 32 + 82 + 02 + 22 + 52 = 122.

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

6446

64465 = 11128881187350154976 :
12 + 12 + 12 + 22 + 82 + 82 + 82 + 12 + 12 + 82 + 72 + 32 + 52 + 02 + 152 + 42 + 92 + 762 = 6446.

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

6447

64472 = 45 + 145 + 185 + 335.

64472 = 41563809, a square with different digits.

Page of Squares : First Upload February 18, 2008 ; Last Revised September 29, 2008
by Yoshio Mimura, Kobe, Japan

6450

64505 = 11163453640312500000 :
12 + 12 + 12 + 62 + 32 + 42 + 52 + 362 + 402 + 312 + 22 + 502 + 02 + 02 + 02 + 02 = 6450.

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

6451

64515 = 11172110164121057251 :
112 + 172 + 22 + 112 + 02 + 162 + 412 + 22 + 102 + 572 + 252 + 12 = 6451.

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

6452

64522 = 1323 + 1713 + 3253.

Page of Squares : First Upload September 29, 2008 ; Last Revised September 29, 2008
by Yoshio Mimura, Kobe, Japan

6453

64532 = 41641209, and 41 + 6412 + 0 * 9 = 6453.

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

6459

64592 = 41718681, a zigzag square.

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

6461

64612 = 2313 + 2433 + 2473.

64615 = 11258971121569108301 :
12 + 122 + 52 + 82 + 92 + 72 + 12 + 122 + 152 + 692 + 12 + 02 + 82 + 302 + 12 = 6461.

Page of Squares : First Upload September 29, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

6463

64632 = 145 + 165 + 165 + 335.

Page of Squares : First Upload September 29, 2008 ; Last Revised September 29, 2008
by Yoshio Mimura, Kobe, Japan

6464

64642 = 41783296, a square with different digits.

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

6467

64672 = 813 + 1883 + 3263.

Page of Squares : First Upload September 29, 2008 ; Last Revised September 29, 2008
by Yoshio Mimura, Kobe, Japan

6468

The integral triangle of sides 14120, 117657, 131761 has square area 64682.

4998k + 6468k + 10542k + 13713k are squares for k = 1,2,3 (1892, 191312, 20360972).

Page of Squares : First Upload June 28, 2011 ; Last Revised October 18, 2011
by Yoshio Mimura, Kobe, Japan

6472

64722 = 464 + 584 + 584 + 624.

Page of Squares : First Upload September 29, 2008 ; Last Revised September 29, 2008
by Yoshio Mimura, Kobe, Japan

6473

1 / 6473 = 0.0001544878727019, 12 + 542 + 482 + 72 + 82 + 72 + 272 + 0192 = 6473.

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

6474

64742 = 1953 + 2183 + 2893.

Page of Squares : First Upload September 29, 2008 ; Last Revised September 29, 2008
by Yoshio Mimura, Kobe, Japan

6475

64752 = 1053 + 2003 + 3203.

Page of Squares : First Upload September 29, 2008 ; Last Revised September 29, 2008
by Yoshio Mimura, Kobe, Japan

6476

64762 = 263 + 953 + 3453.

64762 = 41938576, a zigzag square with different digits.

64762 = 41938576, 4 + 1 * 9 + 3 + 85 * 76 = 4 * 1 + 9 + 3 + 85 * 76 = 6476.

Page of Squares : First Upload February 18, 2008 ; Last Revised September 29, 2008
by Yoshio Mimura, Kobe, Japan

6477

64772 = 733 + 2583 + 2903.

Page of Squares : First Upload September 29, 2008 ; Last Revised September 29, 2008
by Yoshio Mimura, Kobe, Japan

6478

The square root of 6478 is 80.48...., and 80 = 42 + 82.

64785 = 11407874068828166368 :
12 + 12 + 42 + 02 + 72 + 82 + 72 + 402 + 62 + 82 + 82 + 22 + 82 + 12 + 662 + 32 + 62 + 82
= 12 + 12 + 402 + 72 + 82 + 72 + 42 + 02 + 62 + 82 + 82 + 22 + 82 + 12 + 662 + 32 + 62 + 82 = 6478.

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

6480

64802 = 903 + 1083 + 3423.

1232 + 6480 = 1472, 1232 - 6480 = 932.

Komachi equation: 64802 = 92 * 82 / 72 / 62 * 542 / 32 * 2102.

Page of Squares : First Upload September 29, 2008 ; Last Revised August 2, 2011
by Yoshio Mimura, Kobe, Japan

6484

64842 = 333 + 1643 + 3353.

Page of Squares : First Upload September 29, 2008 ; Last Revised September 29, 2008
by Yoshio Mimura, Kobe, Japan

6487

64872 = 42081169, 4 * 20 * 81 + 16 - 9 = 6487.

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

6488

64882 = 1483 + 2283 + 3003.

Page of Squares : First Upload September 29, 2008 ; Last Revised September 29, 2008
by Yoshio Mimura, Kobe, Japan

6489

64882± 3 are primes.

64892 = (22 + 5)(42 + 5)(4722 + 5).

64892 = 493 + 1503 + 3383.

64893 = 273233108169, and 22 + 732 + 22 + 32 + 312 + 02 + 82 + 12 + 62 + 92 = 6489.

Page of Squares : First Upload September 29, 2008 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

6490

64902 = S2(99) + S2(500), where S2(n) = 12 + 22 + 32 + 42 + ... + n2.

6490k + 17110k + 28320k + 35105k are squares for k = 1,2,3 (2952, 486752, 84414252).

Page of Squares : First Upload February 18, 2008 ; Last Revised June 28, 2011
by Yoshio Mimura, Kobe, Japan

6493

64932 = 115 + 195 + 245 + 275 + 285.

Page of Squares : First Upload September 29, 2008 ; Last Revised September 29, 2008
by Yoshio Mimura, Kobe, Japan

6495

64952 = (32 + 6)(16772 + 6).

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

6496

64962 = (32 + 7)(72 + 7)(142 + 7)(152 + 7) = (32 + 7)(72 + 7)(2172 + 7).

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

6497

64972 = 64 + 484 + 544 + 734 = 494 + 564 + 564 + 644.

Page of Squares : First Upload September 29, 2008 ; Last Revised September 29, 2008
by Yoshio Mimura, Kobe, Japan

6498

64982 = 1713 + 2093 + 3043 = 574 + 574 + 574 + 574.

64982 = 42224004, a square with just 3 kinds of even digits.

Page of Squares : First Upload February 18, 2008 ; Last Revised September 29, 2008
by Yoshio Mimura, Kobe, Japan