5400
54002 = (112 - 1)(192 - 1)(262 - 1) = (22 - 1)(32 - 1)(42 - 1)(112 - 1)(262 - 1)
= (22 - 1)(42 - 1)(262 - 1)(312 - 1) = (32 - 1)(42 - 1)(192 - 1)(262 - 1)
= (42 - 1)(52 - 1)(112 - 1)(262 - 1).
54002 = 603 + 2103 + 2703.
752 + 5400 = 1052, 752 - 5400 = 152.
Komachi equation: 54002 = 92 * 82 / 72 * 62 * 52 / 42 / 32 * 2102.
Page of Squares : First Upload September 18, 2008 ; Last Revised December 28, 2013by Yoshio Mimura, Kobe, Japan
5401
54012 = 29170801, a zigzag square.
Page of Squares : First Upload November 26, 2007 ; Last Revised November 26, 2007by Yoshio Mimura, Kobe, Japan
5402
54022 = 29181604, a zigzag square.
Page of Squares : First Upload November 26, 2007 ; Last Revised November 26, 2007by Yoshio Mimura, Kobe, Japan
5403
54032 = 29192409, a zigzag square.
54032± 2 are primes.
54032 = 543 + 1373 + 2983.
Page of Squares : First Upload November 26, 2007 ; Last Revised December 29, 2013by Yoshio Mimura, Kobe, Japan
5405
5405k + 35485k + 74965k + 105045k are squares for k = 1,2,3 (4702, 1339502, 403142502).
Page of Squares : First Upload June 21, 2011 ; Last Revised June 21, 2011by Yoshio Mimura, Kobe, Japan
5406
1 / N = 0.0001849...., and 1849 = 432 for N = 5406, 5407, 5408.
Page of Squares : First Upload November 26, 2007 ; Last Revised November 26, 2007by Yoshio Mimura, Kobe, Japan
5407
54072 = 29235649, 22 + 92 + 22 + 32 + 52 + 62 + 42 + 92 = 162.
Page of Squares : First Upload November 26, 2007 ; Last Revised November 26, 2007by Yoshio Mimura, Kobe, Japan
5408
54082 = 524 + 524 + 524 + 524.
Page of Squares : First Upload September 18, 2008 ; Last Revised September 18, 2008by Yoshio Mimura, Kobe, Japan
5409
54092 = 483 + 1293 + 3003.
Page of Squares : First Upload September 18, 2008 ; Last Revised September 18, 2008by Yoshio Mimura, Kobe, Japan
5412
54122 = (382 + 8)(1422 + 8) = (52 + 8)(62 + 8)(1422 + 8).
54122 = 903 + 1283 + 2983 = 324 + 424 + 444 + 684.
Page of Squares : First Upload September 18, 2008 ; Last Revised December 28, 2013by Yoshio Mimura, Kobe, Japan
5416
54163 = 158867831296, and 12 + 582 + 82 + 62 + 72 + 82 + 312 + 292 + 62 = 5416.
Page of Squares : First Upload December 1, 2008 ; Last Revised December 1, 2008by Yoshio Mimura, Kobe, Japan
5418
54182 = 29273454, a zigzag square.
54182 = (12 + 5)(42 + 5)(92 + 5)(522 + 5) = (22 + 5)(32 + 5)(92 + 5)(522 + 5)
= (32 + 5)(42 + 5)(92 + 5)(342 + 5) = (92 + 5)(112 + 5)(522 + 5) = (92 + 5)(172 + 5)(342 + 5).
by Yoshio Mimura, Kobe, Japan
5419
54192 = 893 + 1303 + 2983.
54192 = 29365561, 2 * 9 + 36 * 5 * 5 * 6 + 1 = 5419.
Page of Squares : First Upload November 26, 2007 ; Last Revised September 18, 2008by Yoshio Mimura, Kobe, Japan
5423
54235 = 4690271924019343343 : 462 + 92 + 02 + 272 + 192 + 242 + 02 + 192 + 32 + 42 + 32 + 342 + 32 = 462 + 92 + 02 + 272 + 192 + 242 + 02 + 192 + 342 + 32 + 32 + 42 + 32 = 5423.
Page of Squares : First Upload December 8, 2008 ; Last Revised December 8, 2008by Yoshio Mimura, Kobe, Japan
5424
54242 = 883 + 1803 + 2843 = 1693 + 2223 + 2393.
Page of Squares : First Upload September 18, 2008 ; Last Revised September 18, 2008by Yoshio Mimura, Kobe, Japan
5426
54262± 3 are primes.
The squaree root of 5426 is 73.661...., and 73 = 62 + 62 + 12.
Page of Squares : First Upload November 26, 2007 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
5427
54272 = 29452329, a zigzag square.
Page of Squares : First Upload November 26, 2007 ; Last Revised November 26, 2007by Yoshio Mimura, Kobe, Japan
5432
54322 = 95 + 95 + 155 + 315.
Page of Squares : First Upload September 18, 2008 ; Last Revised September 18, 2008by Yoshio Mimura, Kobe, Japan
5433
54332 = 973 + 1023 + 3023.
Page of Squares : First Upload September 18, 2008 ; Last Revised September 18, 2008by Yoshio Mimura, Kobe, Japan
5435
The square root of 5435 is 73.7224...., and 73 = 72 + 22 + 22 + 42.
54352 = 29539225, 2 * 9 + 5392 + 25 = 5435.
Page of Squares : First Upload November 26, 2007 ; Last Revised November 26, 2007by Yoshio Mimura, Kobe, Japan
5437
54372 = 29560969, a zigzag square.
Page of Squares : First Upload November 26, 2007 ; Last Revised November 26, 2007by Yoshio Mimura, Kobe, Japan
5438
54382 = 29571844, 22 + 92 + 52 + 72 + 12 + 82 + 42 + 42 = 162.
Page of Squares : First Upload November 26, 2007 ; Last Revised November 26, 2007by Yoshio Mimura, Kobe, Japan
5441
54412 = 29604481, 2 + 9 * 604 - 4 + 8 - 1 = 5441.
Page of Squares : First Upload November 26, 2007 ; Last Revised November 26, 2007by Yoshio Mimura, Kobe, Japan
5443
54432 = 29626249, 29 * 6 / 2 * 62 + 49 = 29 * 62 * 6 / 2 + 49 = 5443.
Page of Squares : First Upload November 26, 2007 ; Last Revised November 26, 2007by Yoshio Mimura, Kobe, Japan
5444
54442 = 29637136, 22 + 92 + 62 + 32 + 72 + 12 + 32 + 62 = 152.
Page of Squares : First Upload November 26, 2007 ; Last Revised November 26, 2007by Yoshio Mimura, Kobe, Japan
5445
54452 = 135 + 195 + 225 + 255 + 265.
54452 = (83 + 84 + 85 + ... + 115)2 + (116 + 117 + 118 + ... + 148)2 + (149 + 150 + 151 + ... + 181)2 + ... + (116 + 117 + 118 + ... + 148)2.
Page of Squares : First Upload November 26, 2007 ; Last Revised September 18, 2008by Yoshio Mimura, Kobe, Japan
5446
54462 = 29658916, 29 * 6 + 58 * 91 - 6 = 5446.
Page of Squares : First Upload November 26, 2007 ; Last Revised November 26, 2007by Yoshio Mimura, Kobe, Japan
5447
The square root of 5447 is 73.803...., and 73 = 82 + 02 + 32.
Page of Squares : First Upload November 26, 2007 ; Last Revised November 26, 2007by Yoshio Mimura, Kobe, Japan
5448
54482 = 29680704, a zigzag square.
Page of Squares : First Upload November 26, 2007 ; Last Revised November 26, 2007by Yoshio Mimura, Kobe, Japan
5449
54492 = 29691601, a zigzag square.
Page of Squares : First Upload November 26, 2007 ; Last Revised November 26, 2007by Yoshio Mimura, Kobe, Japan
5451
The square root of 5451 is 73.83...., and 73 = 82 + 32.
Page of Squares : First Upload November 26, 2007 ; Last Revised November 26, 2007by Yoshio Mimura, Kobe, Japan
5452
54522± 3 are primes.
The square root of 5452 is 73.83...., and 73 = 82 + 32.
Page of Squares : First Upload November 26, 2007 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
5453
Komachi equation: 54532 = 1232 * 4562 * 72 / 82 / 92.
Page of Squares : First Upload October 25, 2010 ; Last Revised October 25, 2010by Yoshio Mimura, Kobe, Japan
5455
54552 = 29757025, 2 / 9 * 7 * 5 * 702 - 5 = 2 + 97 * 7 * 8 + 8 * 4 - 9 = 5457.
Page of Squares : First Upload November 26, 2007 ; Last Revised November 26, 2007by Yoshio Mimura, Kobe, Japan
5457
54572 = 44 + 244 + 324 + 734.
Page of Squares : First Upload September 18, 2008 ; Last Revised September 18, 2008by Yoshio Mimura, Kobe, Japan
5458
5458 = (12 + 22 + 32 + ... + 13642) / (12 + 22 + 32 + ... + 772).
Page of Squares : First Upload November 25, 2008 ; Last Revised November 25, 2008by Yoshio Mimura, Kobe, Japan
5460
54602 = (142 - 1)(3912 - 1).
54602 + 54612 + 54622 + ... + 55122 = 55132 + 55142 + 55152 + ... + 55642.
Komachi equations:
54602 = 92 * 82 * 72 * 652 / 42 / 32 * 22 */ 12 = 982 / 72 * 652 * 42 * 32 / 22 */ 12.
by Yoshio Mimura, Kobe, Japan
5461
1 / 5461 = 0.000183116645303, 182 + 312 + 12 + 62 + 642 + 52 + 32 + 032 = 5461.
Page of Squares : First Upload November 26, 2007 ; Last Revised November 26, 2007by Yoshio Mimura, Kobe, Japan
5463
54632 = 184 + 334 + 364 + 724 = 284 + 384 + 464 + 694.
54634 = 890686361008161, and 82 + 92 + 02 + 62 + 82 + 62 + 362 + 102 + 02 + 82 + 12 + 612 = 5463.
Page of Squares : First Upload September 18, 2008 ; Last Revised December 1, 2008by Yoshio Mimura, Kobe, Japan
5464
54642 = 6192 + 6212 + 6232 + 6252 + 6272 + 6292 + ... + 7452.
Page of Squares : First Upload November 26, 2007 ; Last Revised November 26, 2007by Yoshio Mimura, Kobe, Japan
5465
Loop of length 6 by the function f(N) = b2 + a2 for N = 100b + a:
5465 - 7141 - 6722 - 4973 - 7730 - 6829 - 5465 (Note f(5465) = 542 + 652 = 7141.)
by Yoshio Mimura, Kobe, Japan
5471
54712 = 993 + 2053 + 2733.
Page of Squares : First Upload September 18, 2008 ; Last Revised September 18, 2008by Yoshio Mimura, Kobe, Japan
5472
54722 = (22 + 8)(42 + 8)(122 + 8)(262 + 8).
Komachi equation: 54722 = 92 / 82 * 762 * 52 * 42 * 322 / 102.
Page of Squares : First Upload October 25, 2010 ; Last Revised December 28, 2013by Yoshio Mimura, Kobe, Japan
5475
54752 = 29975625, 2 * 9 + 97 * 56 + 25 = 5475.
Page of Squares : First Upload November 26, 2007 ; Last Revised November 26, 2007by Yoshio Mimura, Kobe, Japan
5476
The square of 74.
54762 = 753 + 1643 + 2933.
5476 is a zigzag square with different digits.
Page of Squares : First Upload November 26, 2007 ; Last Revised September 18, 2008by Yoshio Mimura, Kobe, Japan
5477
54772 = 93 + 923 + 3083.
Page of Squares : First Upload September 18, 2008 ; Last Revised September 18, 2008by Yoshio Mimura, Kobe, Japan
5478
54782 = (22 + 2)(32 + 2)(92 + 2)(742 + 2) = (82 + 2)(92 + 2)(742 + 2).
54782 = 1093 + 2313 + 2543.
54782 = 30008484, 32 + 02 + 02 + 02 + 82 + 42 + 82 + 42 = 132.
Page of Squares : First Upload November 26, 2007 ; Last Revised December 28, 2013by Yoshio Mimura, Kobe, Japan
5480
54802 = 43 + 1603 + 2963 = 793 + 1133 + 3043 = 1903 + 2083 + 2423.
Page of Squares : First Upload September 18, 2008 ; Last Revised September 18, 2008by Yoshio Mimura, Kobe, Japan
5481
54812 = (42 + 5)(162 + 5)(742 + 5).
54812 = 993 + 2273 + 2593 = 124 + 454 + 604 + 604.
Komachi equation: 54812 = 92 * 872 * 62 / 542 * 32 * 212.
Page of Squares : First Upload September 18, 2008 ; Last Revised December 28, 2013by Yoshio Mimura, Kobe, Japan
5484
54842 = 1193 + 1623 + 2893.
Page of Squares : First Upload September 18, 2008 ; Last Revised September 18, 2008by Yoshio Mimura, Kobe, Japan
5487
54872 = 813 + 1463 + 2983.
Page of Squares : First Upload September 18, 2008 ; Last Revised September 18, 2008by Yoshio Mimura, Kobe, Japan
5488
54882 = 284 + 564 + 564 + 564 = 146 + 146 + 146 + 146.
The square root of 5488 ia 74.08103...., and 74 = 02 + 82 + 12 + 02 + 32.
Komachi equations:
54882 = 982 * 72 * 62 * 52 * 42 / 32 * 22 / 102 = 982 * 72 * 62 / 52 * 42 / 32 / 22 * 102
= 982 * 72 / 62 / 52 * 42 * 32 * 22 * 102.
by Yoshio Mimura, Kobe, Japan
5489
54892 = 743 + 1693 + 2923.
1265k + 1529k + 3817k + 5489k are squares for k = 1,2,3 (1102, 69742, 4760142).
Page of Squares : First Upload September 18, 2008 ; Last Revised June 21, 2011by Yoshio Mimura, Kobe, Japan
5491
The square root of 5491 is 74.101282, and 74 = 12 + 02 + 12 + 22 + 82 + 22.
Page of Squares : First Upload November 26, 2007 ; Last Revised November 26, 2007by Yoshio Mimura, Kobe, Japan
5493
54933 = 165740558157, and 162 + 572 + 402 + 52 + 52 + 82 + 152 + 72 = 5493.
Loop of length 35 by the function f(N) = ... + c2 + b2 + a2 where N = ... + 1002c + 100b + a:
5493 - 11565 - 4451 - 4537 - ... - 6736 - 5785 - 10474 - 5493
(Note f(5493) = 542 + 932 = 11565, f(11565) = 12 + 152 + 652 = 4451, etc. See 37)
by Yoshio Mimura, Kobe, Japan
5497
54972 = 30217009, 32 + 02 + 22 + 12 + 72 + 02 + 02 + 92 = 122.
Page of Squares : First Upload November 26, 2007 ; Last Revised November 26, 2007by Yoshio Mimura, Kobe, Japan
5499
54992 = 23 + 1693 + 2943.
54995 = 5028270100947527499 : 52 + 02 + 22 + 82 + 22 + 702 + 102 + 02 + 92 + 42 + 72 + 52 + 22 + 72 + 42 + 92 + 92 = 5499.
Page of Squares : First Upload September 18, 2008 ; Last Revised December 8, 2008by Yoshio Mimura, Kobe, Japan