logo
3500 - 3599

3500

35002 = 703 + 1653 + 1953.

35002 = 12250000, and 1 = 12, 2250000 = 15002.

Page of Squares : First Upload July 2, 2007 ; Last Revised August 18, 2008
by Yoshio Mimura, Kobe, Japan

3501

3501 = 302 + 512.

35012 = 33 + 1833 + 1833.

35012 = 12257001, 1 + 2 - 2 + 5 * 700 * 1 = 1 + 2 / 2 + 5 * 700 - 1 = 1 + 2 / 2 * 5 * 700 * 1
    = 1 - 2 + 2 + 5 * 700 * 1 = 1 - 2 / 2 + 5 * 700 + 1 = 1 * 2 - 2 + 5 * 700 + 1
    = 1 * 2 / 2 + 5 * 700 * 1 = 1 * 2 / 2 * 5 * 700 + 1 = 1 / 2 * 2 + 5 * 700 * 1
    = 1 / 2 * 2 * 5 * 700 + 1 = 1 + 2 * 25 * 70 + 0 * 1 = 1 * 2 * 25 * 70 + 0 + 1 = 3501.

Page of Squares : First Upload July 2, 2007 ; Last Revised August 18, 2008
by Yoshio Mimura, Kobe, Japan

3502

35022 = 1033 + 1573 + 1943.

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

3508

35082 = 75 + 95 + 105 + 125 + 265.

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

3509

35092 = 613 + 733 + 2273.

35092 = (215 + 216 + 217 + ... + 225)2 + (226 + 227 + 228 + ... + 236)2.

35092 = (22 + 7)(10582 + 7).

Page of Squares : First Upload July 2, 2007 ; Last Revised December 21, 2013
by Yoshio Mimura, Kobe, Japan

3510

35102 = (22 + 9)(32 + 9)(92 + 9)(242 + 9) = (22 + 9)(62 + 9)(92 + 9)(152 + 9)
= (32 + 9)(152 + 9)(542 + 9) = (92 + 9)(152 + 9)(242 + 9).

Komachi equations:
35102 = 12 * 22 / 32 / 42 * 52 * 62 * 782 * 92 = 12 / 22 * 32 * 42 * 52 / 62 * 782 * 92
 = 12 * 22 / 32 * 452 / 62 * 782 * 92 = 12 / 22 * 32 * 452 * 62 * 782 / 92.

Page of Squares : First Upload October 4, 2010 ; Last Revised December 21, 2013
by Yoshio Mimura, Kobe, Japan

3511

35112 = 13 + 93 + 2313 = 573 + 1543 + 2043.

23510 = 1 mod 35112.

Page of Squares : First Upload July 2, 2007 ; Last Revised August 18, 2008
by Yoshio Mimura, Kobe, Japan

3512

35122 = 12334144, a square every digit of which is non-zero and smaller than 5.

Page of Squares : First Upload September 7, 2013 ; Last Revised September 7, 2013
by Yoshio Mimura, Kobe, Japan

3515

3515 = (12 + 22 + 32 + ... + 372) / (12 + 22).

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

3520

35202 = (13 + 3)(23 + 3)(53 + 3)(133 + 3).

Page of Squares : First Upload December 21, 2013 ; Last Revised December 21, 2013
by Yoshio Mimura, Kobe, Japan

3522

498k + 942k + 3138k + 3522k are squares for k = 1,2,3 (902, 48362, 2748602).

Page of Squares : First Upload June 3, 2011 ; Last Revised June 3, 2011
by Yoshio Mimura, Kobe, Japan

3523

35222 = 813 + 1073 + 2203 = 1343 + 1573 + 1833.

35222 = 12404484, 1 * 2 + 40 * 44 * 8 / 4 = 1 * 2 * 40 * 44 + 8 / 4 = 3522.

Page of Squares : First Upload July 2, 2007 ; Last Revised August 18, 2008
by Yoshio Mimura, Kobe, Japan

3524

35242 = 324 + 404 + 404 + 504.

35242 = 12418576, 12 + 22 + 42 + 12 + 82 + 52 + 72 + 62 = 142.

Page of Squares : First Upload July 2, 2007 ; Last Revised August 18, 2008
by Yoshio Mimura, Kobe, Japan

3525

The square root of 3525 is 59.371..., and 59 = 32 + 72 + 12.

517k + 893k + 3525k + 3901k are squares for k = 1,2,3 (942, 53582, 3225142).

Page of Squares : First Upload July 2, 2007 ; Last Revised June 3, 2011
by Yoshio Mimura, Kobe, Japan

3528

35282 = 123 + 843 + 2283 = 143 + 493 + 2313 = 213 + 1473 + 2103 = 563 + 1683 + 1963 = 424 + 424 + 424 + 424.

35282 = 12446784, 1 - 2 + 4 / 4 + 6 * 7 * 84 = 12 / 4 / 4 * 6 * 784 = 3528.

35285 = 546566339893690368 : 542 + 62 + 52 + 62 + 62 + 32 + 32 + 92 + 82 + 92 + 32 + 62 + 92 + 02 + 32 + 62 + 82 = 3528.

Komachi equations:
35282 = 92 * 82 * 72 * 62 / 542 * 32 * 212 = 982 * 72 * 62 * 542 / 32 / 212.

Page of Squares : First Upload July 2, 2007 ; Last Revised October 4, 2010
by Yoshio Mimura, Kobe, Japan

3529

3529 is the 8th prime for which the Lendre symbol (a/3529) = 1 for a = 1,2,...,12.

Page of Squares : First Upload July 2, 2007 ; Last Revised July 2, 2007
by Yoshio Mimura, Kobe, Japan

3531

35312 = (24 + 25)2 + (26 + 27)2 + (28 + 29)2 + ... + (264 + 265)2.

Page of Squares : First Upload July 2, 2007 ; Last Revised July 2, 2007
by Yoshio Mimura, Kobe, Japan

3536

35362 = (22 + 4)(32 + 4)(82 + 4)(422 + 4) = (82 + 4)(102 + 4)(422 + 4).

Loop of length 56 by the function f(N) = ... + c2 + b2 + a2 where N = ... + 1002c + 100b + a:
3536 - 2521 - 1066 - 4456 - ... - 7444 - 7412 - 5620 - 3536
(Note f(3536) = 352 + 362 = 2521,   f(2521) = 252 + 212 = 1066, etc. See 41)

Page of Squares : First Upload October 9, 2008 ; Last Revised December 21, 2013
by Yoshio Mimura, Kobe, Japan

3537

35372 = 184 + 244 + 484 + 514.

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

3538

35382 = 723 + 913 + 2253 = 34 + 394 + 394 + 534.

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

3540

The integral triangle of sides 3606, 17405, 20761 has square area 35402.

Page of Squares : First Upload October 11, 2011 ; Last Revised October 11, 2011
by Yoshio Mimura, Kobe, Japan

3541

35412 = 803 + 863 + 2253.

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

3543

1 / 3543 = 0.00028224..., 28224 = 1682.

Page of Squares : First Upload July 2, 2007 ; Last Revised July 2, 2007
by Yoshio Mimura, Kobe, Japan

3545

35452 = 12567025, 12 + 22 + 52 + 62 + 72 + 02 + 22 + 52 = 122.

Page of Squares : First Upload July 2, 2007 ; Last Revised July 2, 2007
by Yoshio Mimura, Kobe, Japan

3546

35462 = (40 + 41 + 42 + ... + 51)2 + (52 + 53 + 54 + ... + 63)2 + (64 + 65 + 66 + ... + 75)2 + ... + (136 + 137 + 138 + ... + 147)2.

Page of Squares : First Upload July 2, 2007 ; Last Revised July 2, 2007
by Yoshio Mimura, Kobe, Japan

3548

35482 = 284 + 444 + 444 + 464.

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

3549

35492± 2 are primes.

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

3550

35502 = 653 + 1703 + 1953.

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

3553

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

Page of Squares : First Upload June 3, 2011 ; Last Revised June 3, 2011
by Yoshio Mimura, Kobe, Japan

3554

35542 = 313 + 1253 + 2203.

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

3555

35552± 2 are primes.

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

3556

35562 = 793 + 973 + 2243.

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

3558

35582 = 12659364, 1 * 2 + 6 * 593 - 6 + 4 = 1 * 2 - 6 + 593 * 6 + 4 = 3558.

Page of Squares : First Upload July 2, 2007 ; Last Revised July 2, 2007
by Yoshio Mimura, Kobe, Japan

3559

1 / 3559 = 0.0002809..., and 2809 = 532.

Page of Squares : First Upload July 2, 2007 ; Last Revised July 2, 2007
by Yoshio Mimura, Kobe, Japan

3560

35602 = 12673600, 1 * 2 - 6 * 7 + 3600 = 3560.

35602 = (22 + 4)(62 + 4)(1992 + 4).

Page of Squares : First Upload July 2, 2007 ; Last Revised December 21, 2013
by Yoshio Mimura, Kobe, Japan

3562

35622± 3 are primes.

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

3564

35642 = 63 + 1493 + 2113 = 333 + 1563 + 2073.

35642 = S2(15) + S2(336), where S2(n) = 12 + 22 + 32 + ... + n2.

35642 = 12702096, 1 / 2 * 7020 + 9 * 6 = 3564.

35642 = (12 + 8)(62 + 8)(102 + 8)(172 + 8) = (22 + 8)(52 + 8)(102 + 8)(172 + 8).

Page of Squares : First Upload July 2, 2007 ; Last Revised December 21, 2013
by Yoshio Mimura, Kobe, Japan

3567

35672 = 43 + 423 + 2333.

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

3569

35692 = 12737761, 1 - 2 + 73 * 7 * 7 - 6 - 1 = 3569.

Page of Squares : First Upload July 2, 2007 ; Last Revised July 2, 2007
by Yoshio Mimura, Kobe, Japan

3570

35702 = 45 + 55 + 105 + 155 + 265.

35702 = 12744900, 1 - 27 - 4 + 4 * 900 = 3570.

35702 + 35712 + 35722 + ... + 36122 = 36132 + 36142 + 36252 + ... + 36542.

3570k + 20706k + 21522k + 47838k are squares for k = 1,2,3 (3062, 565082, 113299562).

Page of Squares : First Upload July 2, 2007 ; Last Revised September 13, 2011
by Yoshio Mimura, Kobe, Japan

3571

35712 = 12752041, 12 + 22 + 72 + 52 + 22 + 02 + 42 + 12 = 102.

35712 = 12752041, 1 / 2 * 7 * 5 * 204 + 1 = 3571.

35715 = 580696556856146851 : 52 + 82 + 02 + 62 + 92 + 62 + 552 + 62 + 82 + 52 + 62 + 12 + 42 + 62 + 82 + 52 + 12 = 3571.

Page of Squares : First Upload July 2, 2007 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

3573

35732 = 12766329, 1 * 2 + 7 + 66 * 3 * 2 * 9 = 3573.

35733 = 45614093517, and 42 + 562 + 12 + 42 + 02 + 92 + 32 + 52 + 172 = 3573.

Page of Squares : First Upload July 2, 2007 ; Last Revised December 1, 2008
by Yoshio Mimura, Kobe, Japan

3574

35742 = 12773476, 1 * 2 * 7 * 7 + 3476 = 3574.

Page of Squares : First Upload July 2, 2007 ; Last Revised July 2, 2007
by Yoshio Mimura, Kobe, Japan

3575

35752 = (188 + 189 + 190 + 191 + 192)2 + (193 + 194 + 195 + 196 + 197)2 + (198 + 199 + 200 + 201 + 202)2 + ... + (238 + 239 + 240 + 241 + 242)2.

35752 = (33 + 34 + 35 + 36 + 37)2 + (38 + 39 + 40 + 41 + 42)2 + (43 + 44 + 45 + 46 + 47)2 + ... + (193 + 194 + 195 + 196 + 197)2.

Page of Squares : First Upload July 2, 2007 ; Last Revised July 2, 2007
by Yoshio Mimura, Kobe, Japan

3576

35762 = (22 + 23 + 24 + ... + 45)2 + (46 + 47 + 48 + ... + 69)2 + (70 + 71 + 72 + ... + 93)2 + ... + (94 + 95 + 96 + ... + 117)2.

Page of Squares : First Upload July 2, 2007 ; Last Revised July 2, 2007
by Yoshio Mimura, Kobe, Japan

3577

154k + 490k + 1708k + 3577k are squares for k = 1,2,3 (772, 39972, 2255472).

Page of Squares : First Upload June 3, 2011 ; Last Revised June 3, 2011
by Yoshio Mimura, Kobe, Japan

3578

35782 = 1133 + 1583 + 1953.

(35782 + 2) = (12 + 2)(32 + 2)(62 + 2)(92 + 2)(112 + 2).

Page of Squares : First Upload July 2, 2007 ; Last Revised August 18, 2008
by Yoshio Mimura, Kobe, Japan

3579

Page of Squares : First Upload January 11, 2011 ; Last Revised January 11, 2011

341 + 21341 + 28731 = 712, 342 + 21342 + 28732 = 35792, 343 + 21343 + 28733 = 1828452  (See 71).

by Yoshio Mimura, Kobe, Japan

3581

35812 = 12823561, 12 + 22 + 82 + 22 + 32 + 52 + 62 + 12 = 122.

Page of Squares : First Upload July 2, 2007 ; Last Revised July 2, 2007
by Yoshio Mimura, Kobe, Japan

3584

35842 = (32 + 7)(52 + 7)(72 + 7)(212 + 7).

A cubic polynomial :
(X + 35842)(X + 38882)(X + 160232) = X3 + 168732X2 + 858658082X + 2232739676162.

Page of Squares : First Upload July 2, 2007 ; Last Revised December 21, 2013
by Yoshio Mimura, Kobe, Japan

3586

35862 = 12859396, 1 + 2 * 8 + 5 + 9 * 396 = 3586.

Page of Squares : First Upload July 2, 2007 ; Last Revised July 2, 2007
by Yoshio Mimura, Kobe, Japan

3587

1 / 3587 = 0.000278784..., and 278784 = 5282.

35872 = 12866569, 1 + 2 * 86 + 6 * 569 = 3587.

Page of Squares : First Upload July 2, 2007 ; Last Revised July 2, 2007
by Yoshio Mimura, Kobe, Japan

3588

35882 = 433 + 1263 + 2213.

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

3590

35902 = 13 + 1063 + 2273.

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

3591

A cubic polynomial :
(X + 6282)(X + 11042)(X + 35912) = X3 + 38092X2 + 46133882X + 24896833922.

35912 = 12895281, 12 + 895 / 2 * 8 - 1 = 3591.

Komachi equation: 35912 = 1232 * 452 - 62 * 782 * 92.

Page of Squares : First Upload July 2, 2007 ; Last Revised October 4, 2010
by Yoshio Mimura, Kobe, Japan

3592

35922 = 783 + 963 + 2263.

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

3597

35972 = 12938409, 12 + 22 + 92 + 32 + 82 + 42 + 02 + 92 = 162.

Page of Squares : First Upload July 2, 2007 ; Last Revised July 2, 2007
by Yoshio Mimura, Kobe, Japan

3599

35992 = 12952801, 1 * 2 * 9 * 5 / 2 * 80 - 1 = 1 / 2 * 9 * 5 * 2 * 80 - 1 = 3599.

Page of Squares : First Upload July 2, 2007 ; Last Revised July 2, 2007
by Yoshio Mimura, Kobe, Japan