5100
51002 = (12 + 9)(52 + 9)(92 + 9)(292 + 9).
Page of Squares : First Upload December 28, 2013 ; Last Revised December 28, 2013by Yoshio Mimura, Kobe, Japan
5101
51012 = 26020201, a zigzag square.
51012 = 26020201, 22 + 62 + 02 + 22 + 02 + 22 + 02 + 12 = 72.
Page of Squares : First Upload October 29, 2007 ; Last Revised October 29, 2007by Yoshio Mimura, Kobe, Japan
5102
51022 = 26030404, a zigzag square.
51022 = 26030404, 22 + 62 + 02 + 32 + 02 + 42 + 02 + 42 = 92.
Page of Squares : First Upload October 29, 2007 ; Last Revised October 29, 2007by Yoshio Mimura, Kobe, Japan
5103
51032 = 184 + 364 + 544 + 634 = 274 + 544 + 544 + 544
51032 = 26040609, a zigzag square.
Komachi equations: 51032 = 92 * 82 * 72 * 62 * 542 / 322 */ 12.
Page of Squares : First Upload October 29, 2007 ; Last Revised October 19, 2010by Yoshio Mimura, Kobe, Japan
5104
51042 = 26050816, a zigzag square.
51042 = (22 + 7)(152 + 7)(1012 + 7).
51045 = 3463804152812929024 : 342 + 62 + 382 + 02 + 42 + 12 + 52 + 282 + 122 + 92 + 292 + 02 + 242 = 5104.
Page of Squares : First Upload October 29, 2007 ; Last Revised December 28, 2013by Yoshio Mimura, Kobe, Japan
5106
51062 = 26071236, 2 * 6 * 71 * 2 * 3 - 6 = 5106.
Page of Squares : First Upload October 29, 2007 ; Last Revised October 29, 2007by Yoshio Mimura, Kobe, Japan
5110
51102 = 45 + 55 + 155 + 165 + 305
Page of Squares : First Upload September 8, 2008 ; Last Revised September 8, 2008by Yoshio Mimura, Kobe, Japan
5112
51122 = 483 + 1043 + 2923 = 64 + 144 + 584 + 624
Page of Squares : First Upload September 8, 2008 ; Last Revised September 8, 2008by Yoshio Mimura, Kobe, Japan
5113
51132 = 84 + 234 + 464 + 684
51132 = 26142769, a zigzag square.
Page of Squares : First Upload October 29, 2007 ; Last Revised September 8, 2008by Yoshio Mimura, Kobe, Japan
5114
51142± 3 are primes.
Loop of length 35 by the function f(N) = ... + c2 + b2 + a2 where N = ... + 1002c + 100b + a:
5114 - 2797 - 10138 - 1446 - ... - 6724 - 5065 - 6725 - 5114
(Note f(5114) = 512 + 142 = 2797, f(2797) = 272 + 972 = 10138, etc. See 37)
by Yoshio Mimura, Kobe, Japan
5116
51162 = 1023 + 1433 + 2813
Page of Squares : First Upload September 8, 2008 ; Last Revised September 8, 2008by Yoshio Mimura, Kobe, Japan
5117
5117 = (12 + 22 + 32 + ... + 422) / (12 + 22).
51172 = 593 + 2313 + 2393
665k + 1421k + 2401k + 5117k are squares for k = 1,2,3 (982, 58662, 3885702).
Page of Squares : First Upload September 8, 2008 ; Last Revised June 17, 2011by Yoshio Mimura, Kobe, Japan
5118
51182 = 174 + 214 + 494 + 674
51182 = 26193924, a zigzag square.
Page of Squares : First Upload October 29, 2007 ; Last Revised September 8, 2008by Yoshio Mimura, Kobe, Japan
5119
51192 = 204 + 204 + 374 + 704
Page of Squares : First Upload September 8, 2008 ; Last Revised September 8, 2008by Yoshio Mimura, Kobe, Japan
5123
51232 = 26245129, 2 - 6 + 2 - 4 + 5129 = 2 - 6 * 2 + 4 + 5129 = 5123.
Page of Squares : First Upload October 29, 2007 ; Last Revised October 29, 2007by Yoshio Mimura, Kobe, Japan
5124
51242± 5 are primes.
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
5125
51252 = 653 + 2303 + 2403
51252 = 26265625, a zigzag square which consists of just 3 kinds of digits.
51253 = 134611328125, and 12 + 342 + 612 + 12 + 32 + 22 + 82 + 122 + 52 = 5125.
Page of Squares : First Upload October 29, 2007 ; Last Revised December 1, 2008by Yoshio Mimura, Kobe, Japan
5129
A cubic polynomial :
(X + 16202)(X + 20792)(X + 44002) = X3 + 51292X2 + 120760202X + 148191120002.
by Yoshio Mimura, Kobe, Japan
5131
51312 = 26327161, and 22 + 62 + 32 + 22 + 712 + 62 + 12.
Page of Squares : First Upload November 25, 2008 ; Last Revised November 25, 2008by Yoshio Mimura, Kobe, Japan
5136
51362 = 333 + 2233 + 2483
51362 = (128 + 129 + 130 + ... + 143)2 + (144 + 145 + 146 + ... + 159)2 + (160 + 161 + 162 + ... + 175)2 + (176 + 177 + 178 + ... + 191)2.
Page of Squares : First Upload October 29, 2007 ; Last Revised September 8, 2008by Yoshio Mimura, Kobe, Japan
5137
51375 = 3577237943395749457 : 32 + 52 + 72 + 72 + 22 + 372 + 92 + 42 + 32 + 32 + 92 + 52 + 72 + 42 + 92 + 42 + 572 = 352 + 72 + 72 + 22 + 372 + 92 + 42 + 32 + 32 + 92 + 52 + 72 + 42 + 92 + 452 + 72 = 32 + 52 + 72 + 72 + 22 + 372 + 92 + 42 + 32 + 32 + 92 + 572 + 42 + 92 + 42 + 52 + 72 = 32 + 572 + 72 + 22 + 372 + 92 + 42 + 32 + 32 + 92 + 52 + 72 + 42 + 92 + 42 + 52 + 72 = 5137.
Page of Squares : First Upload December 8, 2008 ; Last Revised December 8, 2008by Yoshio Mimura, Kobe, Japan
5138
51382 = 94 + 174 + 574 + 634
Page of Squares : First Upload September 8, 2008 ; Last Revised September 8, 2008by Yoshio Mimura, Kobe, Japan
5139
51392 = (52 + 2)(9892 + 2).
Page of Squares : First Upload December 28, 2013 ; Last Revised December 28, 2013by Yoshio Mimura, Kobe, Japan
5144
51442 = 963 + 2003 + 2603
51442 = 26460736, a zigzag square.
Page of Squares : First Upload October 29, 2007 ; Last Revised September 8, 2008by Yoshio Mimura, Kobe, Japan
5145
51452 = 463 + 563 + 2973 = 493 + 983 + 2943
3045k + 3381k + 4305k + 5145k are squares for k = 1,2,3 (1262, 81062, 5318462).
51455 = 3605179521612965625 : 32 + 62 + 02 + 52 + 172 + 92 + 52 + 22 + 12 + 62 + 12 + 292 + 62 + 562 + 252 = 5145.
Page of Squares : First Upload September 8, 2008 ; Last Revised June 17, 2011by Yoshio Mimura, Kobe, Japan
5146
51462 = 26481316, a zigzag square.
Page of Squares : First Upload October 29, 2007 ; Last Revised October 29, 2007by Yoshio Mimura, Kobe, Japan
5147
51472 = 26491609, a zigzag square.
Page of Squares : First Upload October 29, 2007 ; Last Revised October 29, 2007by Yoshio Mimura, Kobe, Japan
5148
51482 = (22 - 1)(102 - 1)(122 - 1)(252 - 1).
51482 = 303 + 1833 + 2733
Page of Squares : First Upload September 8, 2008 ; Last Revised December 28, 2013by Yoshio Mimura, Kobe, Japan
5149
51492 = 26512201, 26 + 5122 + 0 + 1 = 5149.
51495 = 3619215632799800749 : 32 + 62 + 12 + 92 + 212 + 562 + 322 + 72 + 92 + 92 + 82 + 02 + 02 + 72 + 42 + 92 = 5149.
Page of Squares : First Upload October 29, 2007 ; Last Revised December 8, 2008by Yoshio Mimura, Kobe, Japan
5152
138k + 713k + 5152k + 7222k are squares for k = 1,2,3 (1152, 89012, 7167952).
Page of Squares : First Upload June 17, 2011 ; Last Revised June 17, 2011by Yoshio Mimura, Kobe, Japan
5153
51532 = 45 + 115 + 115 + 265 + 275
51532 = 26553409, 22 + 62 + 52 + 52 + 32 + 42 + 02 + 92 = 142.
Page of Squares : First Upload October 29, 2007 ; Last Revised September 8, 2008by Yoshio Mimura, Kobe, Japan
5154
51542 = 26563716, a zigzag square.
51542 = 26563716, 22 + 62 + 52 + 62 + 32 + 72 + 12 + 62 = 142.
Page of Squares : First Upload October 29, 2007 ; Last Revised October 29, 2007by Yoshio Mimura, Kobe, Japan
5156
51562 = 363 + 423 + 2983
51562 = 26584336, 2 * 658 * 4 - 3 * 36 = 5156.
Page of Squares : First Upload October 29, 2007 ; Last Revised September 8, 2008by Yoshio Mimura, Kobe, Japan
5157
51572 = 26594649, a zigzag square.
Page of Squares : First Upload October 29, 2007 ; Last Revised October 29, 2007by Yoshio Mimura, Kobe, Japan
5158
51582 = 26604964, 22 + 62 + 62 + 02 + 42 + 92 + 62 + 42 = 152.
Page of Squares : First Upload October 29, 2007 ; Last Revised October 29, 2007by Yoshio Mimura, Kobe, Japan
5160
51602 = 83 + 1203 + 2923 = 553 + 1373 + 2883 = 683 + 2323 + 2403
Page of Squares : First Upload September 8, 2008 ; Last Revised September 8, 2008by Yoshio Mimura, Kobe, Japan
5161
51612 = 26635921, 22 + 62 + 62 + 32 + 52 + 92 + 22 + 12 = 142.
Page of Squares : First Upload October 29, 2007 ; Last Revised October 29, 2007by Yoshio Mimura, Kobe, Japan
5162
51622 = 26646244, a square with just 3 kinds of even digits.
Page of Squares : First Upload October 29, 2007 ; Last Revised October 29, 2007by Yoshio Mimura, Kobe, Japan
5163
1 / 5163 = 0.0001936..., and 1936 = 442. Also for 5164 and 5165.
1 / 5163 = 0.00019368584156, 192 + 362 + 82 + 582 + 42 + 12 + 52 + 62 = 5163.
Page of Squares : First Upload October 29, 2007 ; Last Revised October 29, 2007by Yoshio Mimura, Kobe, Japan
5166
The integral triangle of sides 5729, 12453, 16810 has square area 51662.
51662 = (12 + 5)(22 + 5)(7032 + 5) = (12 + 5)(32 + 5)(62 + 5)(882 + 5)
= (32 + 5)(42 + 5)(62 + 5)(472 + 5) = (62 + 5)(172 + 5)(472 + 5) = (72 + 5)(7032 + 5).
51664 = 712225645253136,
and 72 + 12 + 22 + 22 + 22 + 52 + 62 + 452 + 22 + 532 + 132 + 62 = 5166.
by Yoshio Mimura, Kobe, Japan
5170
51702 = 7312 + 7322 + 7332 + 7342 + 7352 + ... + 7772.
Page of Squares : First Upload October 29, 2007 ; Last Revised October 29, 2007by Yoshio Mimura, Kobe, Japan
5173
51732 = 26759929, 22 + 62 + 72 + 52 + 92 + 92 + 22 + 92 = 192.
Page of Squares : First Upload October 29, 2007 ; Last Revised October 29, 2007by Yoshio Mimura, Kobe, Japan
5175
51752 = 154 + 204 + 404 + 704 = 154 + 304 + 604 + 604.
Page of Squares : First Upload September 8, 2008 ; Last Revised September 8, 2008by Yoshio Mimura, Kobe, Japan
5176
51762 = 233 + 1693 + 2803.
Page of Squares : First Upload September 8, 2008 ; Last Revised September 8, 2008by Yoshio Mimura, Kobe, Japan
5177
51772 = 94 + 184 + 484 + 684.
Page of Squares : First Upload September 8, 2008 ; Last Revised September 8, 2008by Yoshio Mimura, Kobe, Japan
5179
51792 = 63 + 2333 + 2423.
Page of Squares : First Upload September 8, 2008 ; Last Revised September 8, 2008by Yoshio Mimura, Kobe, Japan
5181
51812 = 743 + 1323 + 2893.
51812 = 26842761, 2 + 6 * 8 * 4 * 27 - 6 + 1 = 2 - 6 + 8 * 4 * 27 * 6 + 1 = 5181.
51814 = 720533818103121, and 72 + 22 + 02 + 532 + 382 + 182 + 102 + 32 + 12 + 212 = 5181,
51814 = 720533818103121, and 72 + 202 + 532 + 382 + 182 + 12 + 02 + 32 + 122 + 12 = 5181.
by Yoshio Mimura, Kobe, Japan
5183
51832 = 26863489, 2 + 6 * 863 + 4 + 8 - 9 = 5183.
51835 = 3740296614814926143 : 32 + 72 + 42 + 02 + 22 + 92 + 62 + 62 + 12 + 482 + 12 + 492 + 22 + 62 + 142 + 32 = 5183.
Page of Squares : First Upload October 29, 2007 ; Last Revised December 8, 2008by Yoshio Mimura, Kobe, Japan
5184
51842 = 1443 + 2883.
The square of 72.
Komachi equations:
51842 = 122 * 32 / 42 * 562 / 72 * 82 * 92,
51842 = 94 * 84 + 74 - 64 / 544 * 34 * 214 = 94 * 84 + 74 / 64 * 544 - 34 * 214
= 94 * 84 + 74 / 64 * 544 / 34 - 214 = 94 * 84 - 74 + 64 / 544 * 34 * 214
= 94 * 84 - 74 / 64 * 544 + 34 * 214 = 94 * 84 - 74 / 64 * 544 / 34 + 214
= 94 * 84 * 74 / 64 * 544 / 34 / 214 = 94 * 84 / 74 * 64 / 544 * 34 * 214
= 984 / 74 * 64 * 544 / 34 / 214.
by Yoshio Mimura, Kobe, Japan
5185
51852 = 553 + 1713 + 2793.
51852 = (199 + 200 + 201 + ... + 215)2 + (216 + 217 + 218 + ... + 232)2 + (233 + 234 + 235 + ... + 249)2 + ... + (216 + 217 + 218 + ... + 232)2.
Page of Squares : First Upload October 29, 2007 ; Last Revised September 8, 2008by Yoshio Mimura, Kobe, Japan
5186
51865 = 3751133858700678176 : 32 + 72 + 52 + 12 + 12 + 32 + 382 + 582 + 72 + 02 + 02 + 62 + 72 + 82 + 12 + 72 + 62 = 5186.
Page of Squares : First Upload December 8, 2008 ; Last Revised December 8, 2008by Yoshio Mimura, Kobe, Japan
5187
51872 = (22 + 3)(42 + 3)(62 + 3)(722 + 3).
51872 = 643 + 653 + 663 + 673 + 683 + 693 + ... + 1053.
Page of Squares : First Upload November 25, 2008 ; Last Revised December 28, 2013by Yoshio Mimura, Kobe, Japan
5188
51882 = 813 + 1403 + 2873 = 24 + 124 + 124 + 724.
Page of Squares : First Upload September 8, 2008 ; Last Revised September 8, 2008by Yoshio Mimura, Kobe, Japan
5191
51912 = 26946481, 2 * 6 - 9 + 4 + 64 * 81 = 2 / 6 * 9 + 4 + 64 * 81 = 5191.
Page of Squares : First Upload October 29, 2007 ; Last Revised October 29, 2007by Yoshio Mimura, Kobe, Japan
5192
51922 = 313 + 903 + 2973
51922 = 26956864, 2 * 6 - 9 + 5 + 6 * 864 = 2 / 6 * 9 + 5 + 6 * 864 = 5192.
Page of Squares : First Upload October 29, 2007 ; Last Revised September 8, 2008by Yoshio Mimura, Kobe, Japan
5193
51932 = 26967249, 2 * 6 * 9 / 6 * 72 * 4 + 9 = 2 / 6 * 9 * 6 * 72 * 4 + 9 = 5193.
Page of Squares : First Upload October 29, 2007 ; Last Revised October 29, 2007by Yoshio Mimura, Kobe, Japan
5194
51942 = (60 + 61 + 62 + 63 + 64 + 65 + 66)2 + (67 + 68 + 69 + 70 + 71 + 72 + 73)2 + (74 + 75 + 76 + 77 + 78 + 79 + 80)2 + ... + (221 + 222 + 223 + 224 + 225 + 226 + 227)2.
Page of Squares : First Upload October 29, 2007 ; Last Revised October 29, 2007by Yoshio Mimura, Kobe, Japan
5199
51992± 2 are primes.
Page of Squares : First Upload December 29, 2013 ; Last Revised December 29, 2013by Yoshio Mimura, Kobe, Japan