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5300 - 5399

5301

53012± 2 are primes.

513k + 1292k + 3382k + 3838k are squares for k = 1,2,3 (952, 53012, 3122652).

Page of Squares : First Upload June 21, 2011 ; Last Revised December 29, 2013
by Yoshio Mimura, Kobe, Japan

5302

1 / 5302 = 0.000188608072425, 182 + 82 + 602 + 82 + 02 + 72 + 242 + 252 = 5302,
1 / 5302 = 0.000188608072425, 182 + 82 + 602 + 82 + 072 + 242 + 252 = 5302.

Page of Squares : First Upload November 19, 2007 ; Last Revised November 19, 2007
by Yoshio Mimura, Kobe, Japan

5303

53032 = 28121809, a zigzag square.

Page of Squares : First Upload November 19, 2007 ; Last Revised November 19, 2007
by Yoshio Mimura, Kobe, Japan

5304

53042 = 28132416, a zigzag square.

Page of Squares : First Upload November 19, 2007 ; Last Revised November 19, 2007
by Yoshio Mimura, Kobe, Japan

5306

53062 = 28153636, a zigzag square.

Page of Squares : First Upload November 19, 2007 ; Last Revised November 19, 2007
by Yoshio Mimura, Kobe, Japan

5313

53132 = 284 + 314 + 484 + 684.

Page of Squares : First Upload September 16, 2008 ; Last Revised September 16, 2008
by Yoshio Mimura, Kobe, Japan

5316

53162 = 703 + 723 + 3023.

Page of Squares : First Upload September 16, 2008 ; Last Revised September 16, 2008
by Yoshio Mimura, Kobe, Japan

5319

53192 = 1693 + 1923 + 2543.

Page of Squares : First Upload September 16, 2008 ; Last Revised September 16, 2008
by Yoshio Mimura, Kobe, Japan

5320

5320 = (12 + 22 + 32 + ... + 35522) / (12 + 22 + 32 + ... + 2032).

53202 = 643 + 1383 + 2943.

152k + 209k + 3344k + 5320k are squares for k = 1,2,3 (952, 62892, 4335612).

Page of Squares : First Upload September 16, 2008 ; Last Revised June 21, 2011
by Yoshio Mimura, Kobe, Japan

5321

53212 = 28313041, 2 - 8 - 3 + 130 * 41 = 5321.

Page of Squares : First Upload November 19, 2007 ; Last Revised November 19, 2007
by Yoshio Mimura, Kobe, Japan

5322

53222 = 1293 + 1523 + 2833.

Page of Squares : First Upload September 16, 2008 ; Last Revised September 16, 2008
by Yoshio Mimura, Kobe, Japan

5323

53232 = 28334329, 22 + 82 + 32 + 32 + 42 + 32 + 22 + 92 = 142.

53232 = 28334329, 2 * 8 * 334 - 3 - 2 * 9 = 5323.

Page of Squares : First Upload November 19, 2007 ; Last Revised November 19, 2007
by Yoshio Mimura, Kobe, Japan

5324

53242 = 2423 + 2423.

Page of Squares : First Upload September 16, 2008 ; Last Revised September 16, 2008
by Yoshio Mimura, Kobe, Japan

5325

53252± 2 are primes.

53252 = 28355625, 2 / 8 * 355 * 6 * 2 * 5 = 5325.

Page of Squares : First Upload November 19, 2007 ; Last Revised December 29, 2013
by Yoshio Mimura, Kobe, Japan

5327

53272 = 44 + 444 + 464 + 674.

53272 = 28376929, a zigzag square.

Page of Squares : First Upload November 19, 2007 ; Last Revised September 16, 2008
by Yoshio Mimura, Kobe, Japan

5329

The square of 73.

53292 = 733 + 1463 + 2923.

Page of Squares : First Upload November 19, 2007 ; Last Revised September 16, 2008
by Yoshio Mimura, Kobe, Japan

5330

53302 = (82 + 1)(92 + 1)(732 + 1) = (32 + 4)(232 + 4)(642 + 4).

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

Page of Squares : First Upload June 21, 2011 ; Last Revised December 28, 2013
by Yoshio Mimura, Kobe, Japan

5331

53312 = 1763 + 1963 + 2493.

Page of Squares : First Upload September 16, 2008 ; Last Revised September 16, 2008
by Yoshio Mimura, Kobe, Japan

5333

53334 = 808884167110321, and 82 + 02 + 82 + 82 + 82 + 42 + 12 + 672 + 112 + 02 + 32 + 212 = 5333.

A cubic polynomial :
(X + 8282)(X + 26882)(X + 45312) = X3 + 53332X2 + 129369482X + 100844835842.

Page of Squares : First Upload November 19, 2007 ; Last Revised December 1, 2008
by Yoshio Mimura, Kobe, Japan

5334

53342 = 28451556, 22 + 82 + 42 + 52 + 12 + 52 + 52 + 62 = 142.

Page of Squares : First Upload November 19, 2007 ; Last Revised November 19, 2007
by Yoshio Mimura, Kobe, Japan

5336

53362 = (42 + 7)(152 + 7)(732 + 7).

53362 = 403 + 683 + 3043 = 403 + 1523 + 2923.

53364 = 810705806626816, and 82 + 12 + 02 + 72 + 02 + 52 + 82 + 02 + 662 + 262 + 82 + 12 + 62 = 5336.

Page of Squares : First Upload September 16, 2008 ; Last Revised December 28, 2013
by Yoshio Mimura, Kobe, Japan

5338

The square root of 5338 is 73.0616...., and 73 = 02 + 62 + 12 + 62.

Page of Squares : First Upload November 19, 2007 ; Last Revised November 19, 2007
by Yoshio Mimura, Kobe, Japan

5340

53402 = 393 + 973 + 3023.

Page of Squares : First Upload September 16, 2008 ; Last Revised September 16, 2008
by Yoshio Mimura, Kobe, Japan

5345

Loop of length 4 :
5345 --- 532 + 452 = 4834 --- 482 + 342 = 3460 --- 342 + 602 = 4756 --- 472 + 562 = 5345

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

5346

53462 = (12 + 2)(222 + 2)(1402 + 2) = (12 + 2)(32 + 2)(52 + 2)(82 + 2)(222 + 2)
= (12 + 2)(42 + 2)(52 + 2)(1402 + 2) = (22 + 2)(52 + 2)(192 + 2)(222 + 2)
= (32 + 2)(52 + 2)(142 + 2)(222 + 2).

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

5347

53472 = 28590409, a zigzag square.

Page of Squares : First Upload November 19, 2007 ; Last Revised November 19, 2007
by Yoshio Mimura, Kobe, Japan

5349

53492 = 3053 + 115 + 57.

Page of Squares : First Upload October 19, 2010 ; Last Revised October 19, 2010
by Yoshio Mimura, Kobe, Japan

5352

53524 = 820473236361216, and 82 + 22 + 02 + 42 + 72 + 322 + 32 + 632 + 62 + 122 + 12 + 62 = 5352.

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

5353

1 / 5353 = 0.000186811133943, 182 + 682 + 112 + 132 + 32 + 92 + 42 + 32 = 5353.

Page of Squares : First Upload November 19, 2007 ; Last Revised November 19, 2007
by Yoshio Mimura, Kobe, Japan

5354

1 / 5354 = 0.00018677624206, 182 + 672 + 72 + 62 + 22 + 42 + 202 + 62 = 5354.

Page of Squares : First Upload November 19, 2007 ; Last Revised November 19, 2007
by Yoshio Mimura, Kobe, Japan

5355

53552 = (22 - 1)(42 - 1)(162 - 1)(502 - 1).

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

5356

53562 = 28686736, a zigzag square.

Page of Squares : First Upload November 19, 2007 ; Last Revised November 19, 2007
by Yoshio Mimura, Kobe, Japan

5358

53582 = 25 + 55 + 75 + 95 + 315.

53582 = 28708164, 2 * 87 + 0 + 81 * 64 = 5358.

141k + 1645k + 2773k + 4277k are squares for k = 1,2,3 (942, 53582, 3225142).
517k + 893k + 3525k + 3901k are squares for k = 1,2,3 (942, 53582, 3225142).

Page of Squares : First Upload November 19, 2007 ; Last Revised June 21, 2011
by Yoshio Mimura, Kobe, Japan

5359

53592 = 983 + 2253 + 2543.

53592 = 28718881, 2 * 87 + 1 + 8 * 8 * 81 = 5359.

713k + 5359k + 10511k + 17273k are squares for k = 1,2,3 (1842, 209302, 25434322).

Page of Squares : First Upload November 19, 2007 ; Last Revised June 21, 2011
by Yoshio Mimura, Kobe, Japan

5360

53605 = 4424089950617600000 : 442 + 242 + 02 + 82 + 92 + 92 + 502 + 62 + 12 + 72 + 62 + 02 + 02 + 02 + 02 + 02 = 5360.

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

5361

53612 = 493 + 633 + 3053.

Page of Squares : First Upload September 16, 2008 ; Last Revised October 19, 2010
by Yoshio Mimura, Kobe, Japan

5363

403k + 961k + 5363k + 8649k are squares for k = 1,2,3 (1242, 102302, 8956522).

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

5364

53642 = 663 + 1603 + 2903.

Komachi equation: 53642 = 92 / 872 * 62 / 52 * 432102.

Page of Squares : First Upload September 16, 2008 ; Last Revised September 16, 2008
by Yoshio Mimura, Kobe, Japan

5365

53652 = (62 + 1)(8822 + 1).

Loop of length 35 by the function f(N) = ... + c2 + b2 + a2 where N = ... + 1002c + 100b + a:
5365 - 7034 - 6056 - 6736 - ... - 1446 - 2312 - 673 - 5365
(Note f(5365) = 532 + 652 = 7034,   f(7034) = 702 + 342 = 6056, etc. See 37)

53655 = 4444763232114353125 : 442 + 442 + 72 + 62 + 32 + 232 + 22 + 12 + 142 + 32 + 52 + 32 + 12 + 252 = 5365.

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

5366

53662 = 28793956, a zigzag square.

Page of Squares : First Upload November 19, 2007 ; Last Revised November 19, 2007
by Yoshio Mimura, Kobe, Japan

5368

53682 = 2243 + 2603 = 64 + 344 + 544 + 664.

Page of Squares : First Upload September 16, 2008 ; Last Revised September 16, 2008
by Yoshio Mimura, Kobe, Japan

5370

53702 = 433 + 1853 + 2823.

53702 = 28836900, 2 - 8 - 8 * 3 + 6 * 900 = 5370.

Page of Squares : First Upload November 19, 2007 ; Last Revised September 16, 2008
by Yoshio Mimura, Kobe, Japan

5371

53712 = 28847641, 2 - 8 + 8 * 4 * 7 * 6 * 4 + 1 = 5371.

Page of Squares : First Upload November 19, 2007 ; Last Revised November 19, 2007
by Yoshio Mimura, Kobe, Japan

5372

53722 = 28858384, 2 * 8 * 8 * 5 * 8 + 3 * 84 = 5372.

Page of Squares : First Upload November 19, 2007 ; Last Revised November 19, 2007
by Yoshio Mimura, Kobe, Japan

5373

53732 = 283 + 783 + 3053.

Page of Squares : First Upload September 16, 2008 ; Last Revised September 16, 2008
by Yoshio Mimura, Kobe, Japan

5375

53752 = 28890625, 2 + 8 + 890 * 6 + 25 = 28 + 890 * 6 + 2 + 5 = 5375.

Page of Squares : First Upload November 19, 2007 ; Last Revised November 19, 2007
by Yoshio Mimura, Kobe, Japan

5376

53762 = (32 - 1)(152 - 1)(1272 - 1).

53762 = 963 + 2243 + 2563.

53762=28901376, a square with different digits.

104 + 5376 = 1242, 104 - 5376 = 682.

Komachi equations:
53762 = 92 * 82 * 72 / 62 * 52 * 42 * 322 / 102 = 982 / 72 * 62 * 52 * 42 * 322 / 102.

Page of Squares : First Upload November 19, 2007 ; Last Revised December 28, 2013
by Yoshio Mimura, Kobe, Japan

5377

53772 = 443 + 2283 + 2573.

Page of Squares : First Upload September 16, 2008 ; Last Revised September 16, 2008
by Yoshio Mimura, Kobe, Japan

5380

53802 = (22 + 23 + 24 + 25 + 26 + 27 + 28 + 29)2 + (30 + 31 + 32 + 33 + 34 + 35 + 36 + 37)2 + (38 + 39 + 40 + 41 + 42 + 43 + 44 + 45)2 + ... + (214 + 215 + 216 + 217 + 218 + 219 + 220 + 221)2.

Page of Squares : First Upload November 19, 2007 ; Last Revised November 19, 2007
by Yoshio Mimura, Kobe, Japan

5382

12 + 22 + 32 + 42 + 52 + ... + 53822 = 51979351515, which consisting of odd digits,
(The second 11-digit sum. There are 3 such sums in all.)

53825 = 4515631221581262432 : 452 + 12 + 52 + 62 + 312 + 22 + 22 + 152 + 82 + 122 + 62 + 22 + 432 + 22 = 452 + 152 + 62 + 312 + 22 + 22 + 12 + 52 + 82 + 122 + 62 + 22 + 432 + 22 = 42 + 52 + 152 + 632 + 122 + 22 + 152 + 82 + 12 + 262 + 22 + 42 + 32 + 22 = 5382.

Page of Squares : First Upload November 19, 2007 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

5383

53832 = 493 + 2113 + 2693 = 523 + 2043 + 2733 = 1053 + 1293 + 2953 = 234 + 384 + 564 + 644.

Page of Squares : First Upload September 16, 2008 ; Last Revised September 16, 2008
by Yoshio Mimura, Kobe, Japan

5384

53845 = 4524027707214823424 : 42 + 522 + 42 + 02 + 272 + 72 + 02 + 72 + 22 + 12 + 42 + 82 + 22 + 342 + 242 = 5384.

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

5385

The square root of 5385 is 73.38...., and 73 = 32 + 82.

Page of Squares : First Upload November 19, 2007 ; Last Revised November 19, 2007
by Yoshio Mimura, Kobe, Japan

5386

The square root of 5386 is 73.38...., and 73 = 32 + 82.

Page of Squares : First Upload November 19, 2007 ; Last Revised November 19, 2007
by Yoshio Mimura, Kobe, Japan

5390

53902 = (12 + 6)(22 + 6)(222 + 6)(292 + 6) = (12 + 6)(222 + 6)(922 + 6)
= (82 + 6)(222 + 6)(292 + 6).

53902 = 23 + 493 + 3073 = 663 + 2253 + 2593.

53902 = 29052100, 2 * 90 + 5210 + 0 = 5390.

5390k + 9482k + 12034k + 12298k are squares for k = 1,2,3 (1982, 203722, 21475082).

Page of Squares : First Upload November 19, 2007 ; Last Revised December 28, 2013
by Yoshio Mimura, Kobe, Japan

5392

53922 = 364 + 484 + 484 + 644.

Page of Squares : First Upload September 16, 2008 ; Last Revised September 16, 2008
by Yoshio Mimura, Kobe, Japan

5394

53942 = 29095236, 2 * 90 * 9 * 5 * 2 / 3 - 6 = 5394.

Page of Squares : First Upload November 19, 2007 ; Last Revised November 19, 2007
by Yoshio Mimura, Kobe, Japan

5395

53952 = 29106025, 2 + 9 * 10 * 60 - 2 - 5 = 2 * 9 * 10 * 60 / 2 - 5 = 5395.

Page of Squares : First Upload November 19, 2007 ; Last Revised November 19, 2007
by Yoshio Mimura, Kobe, Japan

5396

53962 = 803 + 1023 + 3023.

53963 = 157114339136, and 12 + 572 + 12 + 12 + 432 + 32 + 92 + 132 + 62 = 5396.

53962 = 29116816 appears in the decimal expressions of π:
  π = 3.14159•••29116816••• (from the 34309th digit)
  (29116816 is the seventh 8-digit square in the expression of π.)

Page of Squares : First Upload September 16, 2008 ; Last Revised December 1, 2008
by Yoshio Mimura, Kobe, Japan

5397

53972 = 29127609, 22 + 92 + 12 + 22 + 72 + 62 + 02 + 92 = 162.

Page of Squares : First Upload November 19, 2007 ; Last Revised November 19, 2007
by Yoshio Mimura, Kobe, Japan