8301
83012± 2 are primes.
Page of Squares : First Upload January 11, 2014 ; Last Revised January 11, 2014by Yoshio Mimura, Kobe, Japan
8303
83032 = 194 + 384 + 764 + 764.
Page of Squares : First Upload July 7, 2008 ; Last Revised July 7, 2008by Yoshio Mimura, Kobe, Japan
8304
83042± 5 are primes.
83045 = 39485414602020225024 : 392 + 482 + 52 + 412 + 462 + 02 + 22 + 02 + 22 + 02 + 22 + 252 + 02 + 22 + 42 = 8304.
Page of Squares : First Upload December 8, 2008 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
8305
83052 = 68973025, a square with different digits.
1 / 8305 = 0.000120409, and 120409 = 3472
Page of Squares : First Upload July 7, 2008 ; Last Revised July 7, 2008by Yoshio Mimura, Kobe, Japan
8306
83062± 3 are primes.
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
8307
390k + 2262k + 4329k + 6708k are squares for k = 1,2,3 (1172, 83072, 6281732).
Page of Squares : First Upload July 12, 2011 ; Last Revised July 12, 2011by Yoshio Mimura, Kobe, Japan
8308
83082 = 1583 + 3103 + 3283.
Page of Squares : First Upload July 7, 2008 ; Last Revised July 7, 2008by Yoshio Mimura, Kobe, Japan
8313
83132 = 1613 + 2743 + 3543.
Page of Squares : First Upload July 7, 2008 ; Last Revised July 7, 2008by Yoshio Mimura, Kobe, Japan
8315
83152 = 813 + 2983 + 3483 = 1213 + 2783 + 3583.
Page of Squares : First Upload July 7, 2008 ; Last Revised July 7, 2008by Yoshio Mimura, Kobe, Japan
8316
83162 = 423 + 2823 + 3603.
Page of Squares : First Upload July 7, 2008 ; Last Revised July 7, 2008by Yoshio Mimura, Kobe, Japan
8317
83172 = 1773 + 2553 + 3613.
Page of Squares : First Upload July 7, 2008 ; Last Revised July 7, 2008by Yoshio Mimura, Kobe, Japan
8319
83192 = 573 + 1283 + 4063 = 104 + 354 + 384 + 904.
Page of Squares : First Upload July 7, 2008 ; Last Revised July 7, 2008by Yoshio Mimura, Kobe, Japan
8320
83202± 3 are primes.
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
8322
83222 = 69255684, and 6925 / 5 * 6 + 8 + 4 = 8322.
Page of Squares : First Upload July 7, 2008 ; Last Revised July 7, 2008by Yoshio Mimura, Kobe, Japan
8323
83232 = 69272329, a zigzag square.
Page of Squares : First Upload July 7, 2008 ; Last Revised July 7, 2008by Yoshio Mimura, Kobe, Japan
8327
83275 = 40035275672417850407 : 42 + 02 + 02 + 32 + 522 + 72 + 562 + 72 + 242 + 12 + 72 + 82 + 52 + 02 + 402 + 72 = 42 + 02 + 02 + 32 + 52 + 272 + 562 + 72 + 22 + 412 + 72 + 82 + 502 + 42 + 02 + 72 = 402 + 02 + 32 + 522 + 72 + 562 + 72 + 242 + 12 + 72 + 82 + 52 + 02 + 42 + 02 + 72 = 8327.
Page of Squares : First Upload December 8, 2008 ; Last Revised December 8, 2008by Yoshio Mimura, Kobe, Japan
8329
83292 = 173 + 2193 + 3893.
Page of Squares : First Upload July 7, 2008 ; Last Revised July 7, 2008by Yoshio Mimura, Kobe, Japan
8330
83302 = 2033 + 2943 + 3293.
83302 = (366 + 367 + 368 + 369)2 + (370 + 371 + 372 + 373)2 + (374 + 375 + 376 + 377)2 + ... + (462 + 463 + 464 + 465)2.
Page of Squares : First Upload July 7, 2008 ; Last Revised July 7, 2008by Yoshio Mimura, Kobe, Japan
8334
83342 = 69455556, and
6945 * 5 / 5 / 5 * 6 = 6945 / 5 * 5 / 5 * 6 = 6945 / 5 / 5 * 5 * 6 = 8334.
by Yoshio Mimura, Kobe, Japan
8335
83355 = 40227961037165959375 : 42 + 02 + 222 + 72 + 92 + 612 + 02 + 32 + 72 + 162 + 52 + 92 + 592 + 32 + 72 + 52 = 42 + 02 + 222 + 72 + 92 + 612 + 02 + 32 + 72 + 162 + 592 + 52 + 92 + 32 + 72 + 52 = 8335.
Page of Squares : First Upload December 8, 2008 ; Last Revised December 8, 2008by Yoshio Mimura, Kobe, Japan
8338
5698k + 6622k + 8338k + 10318k are squares for k = 1,2,3 (1762, 158842, 14674882).
Page of Squares : First Upload July 12, 2011 ; Last Revised July 12, 2011by Yoshio Mimura, Kobe, Japan
8339
83392 = 69538921, and 695 / 3 * 8 * 9 / 2 - 1 = 8339.
Page of Squares : First Upload July 7, 2008 ; Last Revised July 7, 2008by Yoshio Mimura, Kobe, Japan
8342
83422 = 69588964, 6 + 95 * 88 - 96 / 4 = 8342.
Page of Squares : First Upload July 7, 2008 ; Last Revised July 7, 2008by Yoshio Mimura, Kobe, Japan
8343
83432 = 184 + 634 + 724 + 724.
Page of Squares : First Upload July 7, 2008 ; Last Revised July 7, 2008by Yoshio Mimura, Kobe, Japan
8346
83462 = 69655716, and 62 + 92 + 62 + 52 + 52 + 72 + 12 + 62 = 172.
Page of Squares : First Upload July 7, 2008 ; Last Revised July 7, 2008by Yoshio Mimura, Kobe, Japan
8347
83472 = 69672409, a zigzag square.
Page of Squares : First Upload July 7, 2008 ; Last Revised July 7, 2008by Yoshio Mimura, Kobe, Japan
8349
83492± 2 are primes.
83492 = 69705801, and 62 + 92 + 72 + 02 + 52 + 82 + 02 + 12 = 162.
Page of Squares : First Upload July 7, 2008 ; Last Revised January 11, 2014by Yoshio Mimura, Kobe, Japan
8350
83504 = 4861227006250000, and 42 + 862 + 122 + 272 + 02 + 02 + 62 + 22 + 52 + 02 + 02 + 02 + 02 = 8350.
Page of Squares : First Upload December 1, 2008 ; Last Revised December 1, 2008by Yoshio Mimura, Kobe, Japan
8352
83522 = (62 + 63 + 64 + ... + 93)2 + (94 + 95 + 96 + ... + 125)2 + (126 + 127 + 128 + ... + 157)2 + ... + (158 + 159 + 160 + ... + 189)2.
83522 = 483 + 1203 + 4083.
Komachi equations: 83522 = 92 * 872 / 62 * 52 * 42 * 322 / 102.
Page of Squares : First Upload July 7, 2008 ; Last Revised November 9, 2010by Yoshio Mimura, Kobe, Japan
8353
83535 = 40664216322568456993 : 42 + 02 + 62 + 62 + 42 + 22 + 162 + 32 + 22 + 22 + 52 + 682 + 42 + 562 + 92 + 92 + 32 = 8353.
Page of Squares : First Upload December 8, 2008 ; Last Revised December 8, 2008by Yoshio Mimura, Kobe, Japan
8354
1 / 8354 = 0.000119703136222169, 12 + 192 + 72 + 0312 + 362 + 222 + 212 + 692 = 8354.
Page of Squares : First Upload July 7, 2008 ; Last Revised July 7, 2008by Yoshio Mimura, Kobe, Japan
8356
83565 = 40737292048864715776 : 402 + 72 + 32 + 72 + 292 + 22 + 02 + 482 + 82 + 62 + 42 + 72 + 12 + 572 + 72 + 62 = 8356.
Page of Squares : First Upload December 8, 2008 ; Last Revised December 8, 2008by Yoshio Mimura, Kobe, Japan
8358
83582 = 743 + 1813 + 3993.
83585 = 40786067536627740768 : 42 + 02 + 72 + 82 + 62 + 02 + 62 + 72 + 532 + 662 + 272 + 72 + 42 + 02 + 72 + 62 + 82 = 8358.
Page of Squares : First Upload July 7, 2008 ; Last Revised December 8, 2008by Yoshio Mimura, Kobe, Japan
8360
83605 = 40834889733017600000 : 42 + 02 + 82 + 342 + 82 + 82 + 92 + 72 + 332 + 02 + 12 + 762 + 02 + 02 + 02 + 02 + 02 = 8360.
Page of Squares : First Upload December 8, 2008 ; Last Revised December 8, 2008by Yoshio Mimura, Kobe, Japan
8362
83622± 3 are primes.
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
8364
83642 = (32 + 8)(142 + 8)(1422 + 8).
83642 = 493 + 2313 + 3863.
Page of Squares : First Upload July 7, 2008 ; Last Revised January 11, 2014by Yoshio Mimura, Kobe, Japan
8365
83652 = 69973225, and 62 + 92 + 92 + 72 + 32 + 22 + 22 + 52 = 172.
Page of Squares : First Upload July 7, 2008 ; Last Revised July 7, 2008by Yoshio Mimura, Kobe, Japan
8369
83695 = 41055168535669652849 : 42 + 102 + 52 + 52 + 12 + 62 + 82 + 52 + 32 + 52 + 62 + 692 + 62 + 52 + 282 + 492 = 8369.
Page of Squares : First Upload December 8, 2008 ; Last Revised December 8, 2008by Yoshio Mimura, Kobe, Japan
8374
8374k + 11289k + 22366k + 28196k are squares for k = 1,2,3 (2652, 386372, 59691252).
Page of Squares : First Upload July 12, 2011 ; Last Revised July 12, 2011by Yoshio Mimura, Kobe, Japan
8375
The square root of 8375 is 91.515026...., and 91 = 52 + 12 + 52 + 02 + 22 + 62.
83755 = 41202548431396484375 : 42 + 122 + 02 + 22 + 52 + 42 + 82 + 42 + 32 + 12 + 32 + 92 + 62 + 482 + 42 + 32 + 752 = 42 + 122 + 02 + 22 + 52 + 482 + 42 + 32 + 12 + 32 + 92 + 62 + 42 + 82 + 42 + 32 + 752 = 42 + 122 + 02 + 252 + 42 + 82 + 432 + 12 + 32 + 92 + 642 + 82 + 42 + 372 + 52 = 8375.
Page of Squares : First Upload July 7, 2008 ; Last Revised December 8, 2008by Yoshio Mimura, Kobe, Japan
8376
83762 = (70 + 71 + 72 + ... + 81)2 + (82 + 83 + 84 + ... + 93)2 + (94 + 95 + 96 + ... + 105)2 + ... + (250 + 251 + 252 + ... + 261)2.
83765 = 41227152842752229376 : 42 + 12 + 22 + 22 + 712 + 52 + 282 + 422 + 72 + 52 + 22 + 222 + 92 + 32 + 72 + 62 = 42 + 12 + 22 + 22 + 712 + 52 + 282 + 422 + 72 + 52 + 222 + 22 + 92 + 32 + 72 + 62 = 42 + 12 + 222 + 712 + 52 + 282 + 422 + 72 + 52 + 22 + 22 + 22 + 92 + 32 + 72 + 62 = 8376.
Page of Squares : First Upload July 7, 2008 ; Last Revised December 8, 2008by Yoshio Mimura, Kobe, Japan
8378
83782 = 294 + 374 + 674 + 834.
Page of Squares : First Upload July 7, 2008 ; Last Revised July 7, 2008by Yoshio Mimura, Kobe, Japan
8381
83812 = (332 + 333 + 334 + ... + 348)2 + (349 + 350 + 351 + ... + 365)2.
Page of Squares : First Upload July 7, 2008 ; Last Revised July 7, 2008by Yoshio Mimura, Kobe, Japan
8383
83835 = 41399713035453662143 : 42 + 12 + 392 + 92 + 72 + 12 + 302 + 32 + 52 + 42 + 52 + 32 + 62 + 622 + 12 + 432 = 42 + 12 + 32 + 92 + 92 + 72 + 12 + 302 + 32 + 52 + 42 + 532 + 662 + 22 + 12 + 42 + 32 = 8383.
Page of Squares : First Upload December 8, 2008 ; Last Revised December 8, 2008by Yoshio Mimura, Kobe, Japan
8384
83842 = 70291456, a square with different digits.
83842 = 273 + 2933 + 3563 = 1523 + 2723 + 3603.
Page of Squares : First Upload July 7, 2008 ; Last Revised July 7, 2008by Yoshio Mimura, Kobe, Japan
8385
83852 = 783 + 973 + 4103.
83854 = 4943246502650625, and 42 + 92 + 432 + 22 + 462 + 52 + 02 + 22 + 652 + 02 + 62 + 22 + 52 = 8385.
Page of Squares : First Upload July 7, 2008 ; Last Revised December 1, 2008by Yoshio Mimura, Kobe, Japan
8390
83902 = S2(4) + S2(595), where S2(n) = 12 + 22 + 32 + 42 + ... + n2.
Page of Squares : First Upload July 7, 2008 ; Last Revised July 7, 2008by Yoshio Mimura, Kobe, Japan
8393
(83932 + 1) = (22 + 1)(52 + 1)(62 + 1)(102 + 1)(122 + 1) = (12 + 1)(62 + 1)(82 + 1)(102 + 1)(122 + 1).
83934 = 4962138621117601, and 42 + 92 + 62 + 212 + 382 + 62 + 212 + 112 + 762 + 02 + 12 = 8393.
83935 = 41647229447040025193 : 42 + 162 + 42 + 722 + 292 + 42 + 42 + 72 + 02 + 402 + 02 + 22 + 52 + 192 + 32 = 42 + 162 + 472 + 222 + 92 + 42 + 42 + 702 + 42 + 02 + 02 + 22 + 52 + 192 + 32 = 8393.
Page of Squares : First Upload July 7, 2008 ; Last Revised December 8, 2008by Yoshio Mimura, Kobe, Japan
8394
83942 = 70459236, a square with different digits.
83942 = 70459236, and 70 * 4 * 5 * 9 * 2 / 3 - 6 = 8394.
Page of Squares : First Upload July 7, 2008 ; Last Revised July 7, 2008by Yoshio Mimura, Kobe, Japan
8396
83962 = 70492816, a square with different digits.
83965 = 41721714755492350976 : 42 + 12 + 72 + 212 + 72 + 12 + 472 + 552 + 492 + 22 + 32 + 52 + 02 + 92 + 72 + 62 = 8396.
Page of Squares : First Upload July 7, 2008 ; Last Revised December 8, 2008by Yoshio Mimura, Kobe, Japan
8397
83972 = 1023 + 2493 + 3783.
Page of Squares : First Upload July 7, 2008 ; Last Revised July 7, 2008by Yoshio Mimura, Kobe, Japan
8399
83992 = 70543201, and 70 * 5 * 4 * 3 * 2 + 0 - 1 = 8399.
Page of Squares : First Upload July 7, 2008 ; Last Revised July 7, 2008by Yoshio Mimura, Kobe, Japan