7200
72002 = (32 - 1)(92 - 1)(112 - 1)(262 - 1)= (42 - 1)(92 - 1)(112 - 1)(192 - 1)
= (92 - 1)(262 - 1)(312 - 1).
72002 = 1063 + 2523 + 3263 = 604 + 604 + 604 + 604.
Page of Squares : First Upload April 14, 2008 ; Last Revised January 11, 2014by Yoshio Mimura, Kobe, Japan
7201
72012 = 51854401, and 5 * 18 * 5 * 4 * 4 + 0 + 1 = 7201.
Page of Squares : First Upload April 14, 2008 ; Last Revised April 14, 2008by Yoshio Mimura, Kobe, Japan
7202
72022± 3 are primes.
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
7205
72055 = 19416454336822503125 :
192 + 412 + 62 + 452 + 432 + 32 + 62 + 82 + 222 + 52 + 02 + 32 + 12 + 252
= 192 + 42 + 162 + 452 + 42 + 32 + 362 + 82 + 222 + 502 + 32 + 122 + 52 = 7205.
by Yoshio Mimura, Kobe, Japan
7209
72092 = 51969681, a zigzag square.
72092± 2 are primes.
72095 = 19470411381029855049 :
12 + 92 + 472 + 02 + 42 + 12 + 12 + 382 + 102 + 292 + 82 + 52 + 52 + 02 + 492
= 12 + 92 + 42 + 702 + 412 + 132 + 82 + 12 + 02 + 22 + 92 + 82 + 52 + 52 + 02 + 42 + 92 = 7209.
by Yoshio Mimura, Kobe, Japan
7210
72102 = (22 + 6)(322 + 6)(712 + 6).
72102 = 51984100, and 51984 = 2282, 100 = 102.
Page of Squares : First Upload April 14, 2008 ; Last Revised January 11, 2014by Yoshio Mimura, Kobe, Japan
7212
72124 = 2705346343547136,
and 272 + 02 + 52 + 32 + 42 + 632 + 42 + 32 + 52 + 472 + 132 + 62 = 7212.
by Yoshio Mimura, Kobe, Japan
7213
72134 = 2706847125062161,
and 22 + 72 + 02 + 682 + 472 + 12 + 22 + 52 + 02 + 62 + 22 + 162 + 12 = 7213.
by Yoshio Mimura, Kobe, Japan
7214
72142 = 52041796, a square with different digits.
72145 = 19538026301953113824 :
12 + 92 + 52 + 32 + 802 + 22 + 62 + 32 + 02 + 192 + 52 + 32 + 12 + 132 + 82 + 22 + 42
= 192 + 52 + 32 + 802 + 22 + 62 + 32 + 02 + 12 + 92 + 52 + 32 + 12 + 132 + 82 + 22 + 42 = 7214.
by Yoshio Mimura, Kobe, Japan
7215
72152 = (216 + 217 + 218 + 219 + 220)2 + (221 + 222 + 223 + 224 + 225)2 + (226 + 227 + 228 + 229 + 230)2 + ... + (341 + 342 + 343 + 344 + 345)2.
Page of Squares : First Upload April 14, 2008 ; Last Revised April 14, 2008by Yoshio Mimura, Kobe, Japan
7218
72182 = 1303 + 2013 + 3473 = 34 + 514 + 694 + 694.
Page of Squares : First Upload April 14, 2008 ; Last Revised April 14, 2008by Yoshio Mimura, Kobe, Japan
7222
138k + 713k + 5152k + 7222k are squares for k = 1,2,3 (1152, 89012, 7167952).
Page of Squares : First Upload July 8, 2011 ; Last Revised July 8, 2011by Yoshio Mimura, Kobe, Japan
7223
72232 = 184 + 214 + 384 + 844.
Page of Squares : First Upload April 14, 2008 ; Last Revised April 14, 2008by Yoshio Mimura, Kobe, Japan
7224
72242 = (12 + 3)(22 + 3)(32 + 3)(132 + 3)(302 + 3) = (12 + 3)(92 + 3)(132 + 3)(302 + 3)
= (32 + 3)(132 + 3)(1592 + 3) = (32 + 3)(52 + 3)(132 + 3)(302 + 3).
72242 = 2103 + 2533 + 2993.
Page of Squares : First Upload April 14, 2008 ; Last Revised January 11, 2014by Yoshio Mimura, Kobe, Japan
7225
The square of 85.
1 / 7225 = 0.0001384, 132 + 842 = 7225.
Page of Squares : First Upload April 14, 2008 ; Last Revised April 14, 2008by Yoshio Mimura, Kobe, Japan
7226
72262 = 52215076, and 52 + 22 + 22 + 12 + 52 + 02 + 72 + 62 = 122.
Page of Squares : First Upload April 14, 2008 ; Last Revised April 14, 2008by Yoshio Mimura, Kobe, Japan
7227
72272 = 52229529, a square with just 3 kinds of digits.
Page of Squares : First Upload April 14, 2008 ; Last Revised April 14, 2008by Yoshio Mimura, Kobe, Japan
7228
72282 = 913 + 1423 + 3653.
72285 = 19728347970381626368 :
192 + 72 + 22 + 82 + 32 + 472 + 92 + 72 + 02 + 32 + 82 + 162 + 22 + 632 + 62 + 82 = 7228.
by Yoshio Mimura, Kobe, Japan
7229
72295 = 19741998916420227149 :
192 + 72 + 412 + 92 + 92 + 82 + 92 + 12 + 642 + 202 + 22 + 22 + 72 + 142 + 92
= 12 + 92 + 742 + 192 + 92 + 82 + 92 + 12 + 62 + 42 + 202 + 222 + 72 + 12 + 42 + 92
= 192 + 742 + 12 + 92 + 92 + 82 + 92 + 12 + 62 + 42 + 202 + 222 + 72 + 12 + 42 + 92 = 7229.
by Yoshio Mimura, Kobe, Japan
7230
The square root of 7230 is 85.029...., and 85 = 02 + 22 + 92.
7230 = 362 + 372 + 382 + 392 + 402 = 412 + 422 + 432 + 442.
72302 = 340 x 341 + 341 x 342 + 342 x 343 + ... + 580 x 581.
72302 = 1193 + 1723 + 3573.
Page of Squares : First Upload April 14, 2008 ; Last Revised September 1, 2011by Yoshio Mimura, Kobe, Japan
7235
72355 = 19824063368475021875 :
12 + 92 + 82 + 242 + 02 + 62 + 332 + 62 + 82 + 472 + 502 + 212 + 82 + 72 + 52 = 7235.
by Yoshio Mimura, Kobe, Japan
7237
72372 = 52374169, a square with different digits.
Page of Squares : First Upload April 14, 2008 ; Last Revised April 14, 2008by Yoshio Mimura, Kobe, Japan
7238
The square root of 7238 is 85.076...., and 85 = 02 + 72 + 62.
Page of Squares : First Upload April 14, 2008 ; Last Revised April 14, 2008by Yoshio Mimura, Kobe, Japan
7239
72392 = 52403121, a zigzag square.
Page of Squares : First Upload April 14, 2008 ; Last Revised April 14, 2008by Yoshio Mimura, Kobe, Japan
7240
72402 = 1593 + 1643 + 3533.
Page of Squares : First Upload April 14, 2008 ; Last Revised April 14, 2008by Yoshio Mimura, Kobe, Japan
7242
204k + 3162k + 7242k + 12801k are squares for k = 1,2,3 (1532, 150452, 15840092).
Page of Squares : First Upload July 8, 2011 ; Last Revised July 8, 2011by Yoshio Mimura, Kobe, Japan
7244
1 / 7244 = 0.000138045278, 12 + 32 + 802 + 42 + 52 + 272 + 82 = 7244.
72442 = 1023 + 2383 + 3363.
Page of Squares : First Upload April 14, 2008 ; Last Revised April 14, 2008by Yoshio Mimura, Kobe, Japan
7245
72452 = (22 - 1)(82 - 1)(222 - 1)(242 - 1) = (202 + 5)(3602 + 5).
1 / 7245 = 0.000138026, 132 + 802 + 262 = 7245.
Page of Squares : First Upload April 14, 2008 ; Last Revised January 11, 2014by Yoshio Mimura, Kobe, Japan
7246
72462 = 193 + 1763 + 3613.
Page of Squares : First Upload April 14, 2008 ; Last Revised April 14, 2008by Yoshio Mimura, Kobe, Japan
7249
72495 = 20016608673536911249 :
202 + 02 + 162 + 602 + 82 + 62 + 72 + 352 + 362 + 92 + 12 + 122 + 42 + 92 = 7249.
by Yoshio Mimura, Kobe, Japan
7250
72502 = 52562500, and 5 * 25 * 62 - 500 = 7250.
72502 = 55 + 155 + 205 + 305 + 305.
Page of Squares : First Upload April 14, 2008 ; Last Revised April 14, 2008by Yoshio Mimura, Kobe, Japan
7251
72513 = 381235834251, and 382 + 122 + 352 + 82 + 32 + 422 + 512 = 7251.
Loop of length 56 by the function f(N) = ... + c2 + b2 + a2 where N = ... + 1002c + 100b + a:
7251 - 7785 - 13154 - 3878 - ... - 3650 - 3796 - 10585 - 7251
(Note f(7251) = 722 + 512 = 7785, f(7785) = 772 + 852 = 13154, etc. See 41)
by Yoshio Mimura, Kobe, Japan
7257
5251k + 7257k + 15635k + 27553k are squares for k = 1,2,3 (2362, 329222, 50265642).
Page of Squares : First Upload July 8, 2011 ; Last Revised July 8, 2011by Yoshio Mimura, Kobe, Japan
7259
72592 = 52693081, a square with different digits.
Page of Squares : First Upload April 14, 2008 ; Last Revised April 14, 2008by Yoshio Mimura, Kobe, Japan
7260
72602 = 1103 + 1983 + 3523.
72602 + 72612 + 72622 + ... + 73202 = 73212 + 73222 + 73232 + ... + 73802.
Page of Squares : First Upload April 14, 2008 ; Last Revised September 16, 2011by Yoshio Mimura, Kobe, Japan
7261
72614 = 2779622042738641,
and 22 + 72 + 72 + 92 + 622 + 22 + 02 + 42 + 22 + 72 + 382 + 62 + 412 = 7261.
by Yoshio Mimura, Kobe, Japan
7267
72672 = 393 + 1193 + 3713.
Page of Squares : First Upload April 14, 2008 ; Last Revised April 14, 2008by Yoshio Mimura, Kobe, Japan
7268
72682 = 124 + 344 + 364 + 844.
72685 = 20280310184252269568 :
202 + 282 + 02 + 32 + 12 + 02 + 182 + 422 + 52 + 22 + 262 + 92 + 562 + 82 = 7268.
by Yoshio Mimura, Kobe, Japan
7269
72692 = 52838361, a zigzag square.
Page of Squares : First Upload April 14, 2008 ; Last Revised April 14, 2008by Yoshio Mimura, Kobe, Japan
7271
72712 = 52867441, and 528 + 6744 - 1 = 7271.
Page of Squares : First Upload April 14, 2008 ; Last Revised April 14, 2008by Yoshio Mimura, Kobe, Japan
7272
72722 = 52881984, 5288 + 1984 = 7272.
72722 = 583 + 723 + 3743.
Page of Squares : First Upload April 14, 2008 ; Last Revised April 14, 2008by Yoshio Mimura, Kobe, Japan
7273
72735 = 20350165140742547593 :
22 + 02 + 352 + 02 + 162 + 52 + 12 + 402 + 72 + 422 + 52 + 472 + 52 + 92 + 32 = 7273.
by Yoshio Mimura, Kobe, Japan
7275
The square root of 7275 is 85.29...., and 85 = 22 + 92.
Page of Squares : First Upload April 14, 2008 ; Last Revised April 14, 2008by Yoshio Mimura, Kobe, Japan
7276
72762 = 52940176, a square with different digits.
The square root of 7276 is 85.29...., and 85 = 22 + 92.
Page of Squares : First Upload April 14, 2008 ; Last Revised April 14, 2008by Yoshio Mimura, Kobe, Japan
7278
72782 = 52969284, a zigzag square.
72784 = 2805745047472656,
and 282 + 02 + 52 + 72 + 452 + 02 + 42 + 72 + 42 + 72 + 22 + 652 + 62 = 7278.
72785 = 20420212455505990368 :
202 + 422 + 02 + 212 + 242 + 52 + 52 + 502 + 52 + 92 + 92 + 02 + 362 + 82 = 7278.
by Yoshio Mimura, Kobe, Japan
7280
Komachi equations: 72802 = 982 / 72 * 652 / 42 * 322 */ 12.
Page of Squares : First Upload November 5, 2010 ; Last Revised November 5, 2010by Yoshio Mimura, Kobe, Japan
7281
72812 = 2143 +2763 + 2813.
Page of Squares : First Upload April 14, 2008 ; Last Revised April 14, 2008by Yoshio Mimura, Kobe, Japan
7283
72835 = 20490452525539396643 :
22 + 02 + 42 + 92 + 02 + 42 + 522 + 522 + 52 + 52 + 32 + 92 + 392 + 62 + 62 + 42 + 32
= 22 + 02 + 42 + 92 + 02 + 42 + 522 + 522 + 52 + 52 + 392 + 32 + 92 + 62 + 62 + 42 + 32 = 7283.
by Yoshio Mimura, Kobe, Japan
7284
72842 = 15 + 165 + 235 + 235 + 335.
Page of Squares : First Upload April 14, 2008 ; Last Revised April 14, 2008by Yoshio Mimura, Kobe, Japan
7285
The square root of 7285 is 85.35221145...., and 85 = 32 + 52 + 22 + 22 + 12 + 12 + 42 + 52.
Page of Squares : First Upload April 14, 2008 ; Last Revised April 14, 2008by Yoshio Mimura, Kobe, Japan
7286
72862 = 53085796, and 52 + 32 + 02 + 82 + 52 + 72 + 92 + 62 = 172.
72865 = 20532689255444046176 :
202 + 52 + 32 + 262 + 82 + 92 + 22 + 52 + 52 + 442 + 402 + 462 + 172 + 62 = 7286.
by Yoshio Mimura, Kobe, Japan
7288
72884 = 2821197276123136,
and 22 + 822 + 12 + 192 + 72 + 22 + 72 + 62 + 12 + 22 + 32 + 12 + 32 + 62 = 7288.
by Yoshio Mimura, Kobe, Japan
7290
72902 = 3243 + 275 + 97.
Page of Squares : First Upload November 5, 2010 ; Last Revised November 5, 2010by Yoshio Mimura, Kobe, Japan
7291
72912 = 53158681, and 52 + 32 + 12 + 52 + 82 + 62 + 82 + 12 = 152.
Page of Squares : First Upload April 14, 2008 ; Last Revised April 14, 2008by Yoshio Mimura, Kobe, Japan
7293
1 / 7293 = 0.0001371177841, 132 + 712 + 172 + 72 + 82 + 412 = 7293.
72932 = 2162 + 2172 + 2182 + 2192 + ... + 5532.
Page of Squares : First Upload April 14, 2008 ; Last Revised April 14, 2008by Yoshio Mimura, Kobe, Japan
7295
72955 = 20659817515160309375 :
202 + 62 + 52 + 92 + 82 + 172 + 52 + 12 + 512 + 602 + 32 + 02 + 92 + 32 + 72 + 52
= 202 + 62 + 52 + 92 + 82 + 172 + 512 + 52 + 12 + 602 + 32 + 02 + 92 + 32 + 72 + 52 = 7295.
by Yoshio Mimura, Kobe, Japan
7296
72962 = 53231616, and 52 + 32 + 22 + 32 + 12 + 62 + 12 + 62 = 112.
72962 = 403 + 1433 + 3693.
Komachi equations:
72962 = 92 * 82 * 762 * 52 * 42 / 32 * 22 / 102 = 92 * 82 * 762 / 52 * 42 / 32 / 22 * 102.
by Yoshio Mimura, Kobe, Japan
7297
72972 = 84 + 374 + 684 + 744.
72975 = 20688153565644656257 :
202 + 62 + 82 + 82 + 152 + 352 + 62 + 52 + 62 + 442 + 62 + 562 + 22 + 52 + 72
= 202 + 62 + 82 + 82 + 152 + 352 + 62 + 562 + 442 + 62 + 52 + 62 + 22 + 52 + 72 = 7297.
by Yoshio Mimura, Kobe, Japan
7297
72982 = (132 + 9)(5472 + 9).
Page of Squares : First Upload January 11, 2014 ; Last Revised January 11, 2014by Yoshio Mimura, Kobe, Japan