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7000 - 7099

7002

70025 = 16831023723920560032 :
162 + 82 + 312 + 02 + 22 + 32 + 72 + 232 + 92 + 202 + 52 + 602 + 02 + 322
= 162 + 82 + 312 + 02 + 232 + 72 + 22 + 32 + 92 + 202 + 52 + 602 + 02 + 322 = 7002.

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

7005

70053 = 343735525125, and 342 + 372 + 352 + 52 + 22 + 512 + 252 = 7005.

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

7006

70062 = 93 + 1943 + 3473.

70063 = 343882756216, and 342 + 382 + 82 + 272 + 562 + 212 + 62 = 7006.

Page of Squares : First Upload March 31, 2008 ; Last Revised December 1, 2008
by Yoshio Mimura, Kobe, Japan

7007

70072 = (263 + 264 + 265 + 266 + 267 + 268 + 269)2 + (270 + 271 + 272 + 273 + 274 + 275 + 276)2 + (277 + 278 + 279 + 280 + 281 + 282 + 283)2 + ... + (333 + 334 + 335 + 336 + 337 + 338 + 339)2.

70072 = (46 + 47 + 48 + 49 + 50 + 51 + 52)2 + (53 + 54 + 55 + 56 + 57 + 58 + 59)2 + (60 + 61 + 62 + 63 + 64 + 65 + 66)2 + ... + (270 + 271 + 272 + 273 + 274 + 275 + 276)2.

Page of Squares : First Upload March 31, 2008 ; Last Revised March 31, 2008
by Yoshio Mimura, Kobe, Japan

7008

70082 = (157 + 158 + 159)2 + (160 + 161 + 162)2 + ... + (373 + 374 + 375)2.

70082 = 13 + 1913 + 3483 = 23 + 2283 + 3343 = 83 + 2403 + 3283.

Page of Squares : First Upload March 31, 2008 ; Last Revised March 31, 2008
by Yoshio Mimura, Kobe, Japan

7009

70093 = 344324701729, and 32 + 442 + 32 + 22 + 42 + 702 + 12 + 72 + 22 + 92 = 7009.

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

7010

70102 = 15 + 195 + 225 + 285 + 305.

Page of Squares : First Upload March 31, 2008 ; Last Revised March 31, 2008
by Yoshio Mimura, Kobe, Japan

7018

70182 = 49252324, a zigzag square.

70185 = 17024204181356049568 :
12 + 72 + 02 + 22 + 42 + 22 + 02 + 42 + 12 + 82 + 12 + 352 + 62 + 02 + 492 + 562 + 82
= 172 + 02 + 242 + 202 + 42 + 12 + 82 + 12 + 32 + 52 + 62 + 02 + 492 + 562 + 82
= 172 + 02 + 242 + 202 + 42 + 12 + 82 + 12 + 32 + 562 + 02 + 492 + 52 + 62 + 82 = 7018.

58k + 7018k + 10034k + 13166k are squares for k = 1,2,3 (1742, 179802, 19073882).

Page of Squares : First Upload March 31, 2008 ; Last Revised July 5, 2011
by Yoshio Mimura, Kobe, Japan

7020

70202 = (12 + 9)(22 + 9)(32 + 9)(92 + 9)(152 + 9) = (32 + 9)(92 + 9)(112 + 9)(152 + 9).

70202 = 704 x 705 + 706 x 707 + 708 x 709 + 710 x 711 + ... + 862 x 863.

70202 = 1123 + 2103 + 3383 = 1703 + 2343 + 3163.

Page of Squares : First Upload March 31, 2008 ; Last Revised January 11, 2014
by Yoshio Mimura, Kobe, Japan

7021

70212 + 70222 + 70232 + ... + 70802 = 70812 + 70822 + 70832 + ... + 71392.

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

7023

70232± 2 are primes.

Page of Squares : First Upload January 11, 2014 ; Last Revised January 11, 2014
by Yoshio Mimura, Kobe, Japan

7025

70252 = 49350625, a zigzag square.

70252 = 49350625, and 42 + 92 + 32 + 52 + 02 + 62 + 22 + 52 = 142.

Page of Squares : First Upload March 31, 2008 ; Last Revised March 31, 2008
by Yoshio Mimura, Kobe, Japan

7026

70262 = 613 + 1593 + 3563.

70265 = 17121457308246041376 :
12 + 72 + 122 + 142 + 52 + 72 + 302 + 82 + 242 + 602 + 42 + 12 + 372 + 62 = 7026.

Page of Squares : First Upload March 31, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

7028

The square root of 7028 is 83.8331...., and 83 = 82 + 32 + 32 + 12.

70282 = 2383 + 2463 + 2763.

70284 = 2439647111270656,
and 22 + 432 + 92 + 62 + 42 + 72 + 12 + 12 + 12 + 272 + 02 + 652 + 62 = 7028.

490k + 1022k + 1274k + 6818k are squares for k = 1,2,3 (982, 70282, 5658522).

Page of Squares : First Upload March 31, 2008 ; Last Revised July 5, 2011
by Yoshio Mimura, Kobe, Japan

7029

165k + 7029k + 9273k + 22737k are squares for k = 1,2,3 (1982, 255422, 35915222).

Page of Squares : First Upload July 5, 2011 ; Last Revised July 5, 2011
by Yoshio Mimura, Kobe, Japan

7031

70312 = 49434961, and 42 + 92 + 42 + 32 + 42 + 92 + 62 + 12 = 162.

Page of Squares : First Upload March 31, 2008 ; Last Revised March 31, 2008
by Yoshio Mimura, Kobe, Japan

7032

70322 = 49449024, and 4 * 9 * 4 * 49 + 0 - 24 = 49 * 4 * 4 * 9 + 0 - 24 = 7032.

Page of Squares : First Upload March 31, 2008 ; Last Revised March 31, 2008
by Yoshio Mimura, Kobe, Japan

7033

2080k + 3497k + 4004k + 4108k are squares for k = 1,2,3 (1172, 70332, 4304432).

Page of Squares : First Upload July 5, 2011; Last Revised July 5, 2011
by Yoshio Mimura, Kobe, Japan

7034

Loop of length 35 by the function f(N) = ... + c2 + b2 + a2 where N = ... + 1002c + 100b + a:
7034 - 6056 - 6736 - 5785 - ... - 2312 - 673 - 5365 - 7034
(Note f(7034) = 702 + 342 = 6056,   f(6056) = 602 + 562 = 6736, etc. See 37)

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

7035

70352 = 183 + 2663 + 3133.

Page of Squares : First Upload March 31, 2008 ; Last Revised March 31, 2008
by Yoshio Mimura, Kobe, Japan

7036

70362 = 30 + 31 + 32 + 33 + 34 + 35 + 37 + 39 + 310 + 313 + 314 + 316.

Page of Squares : First Upload August 30, 2011 ; Last Revised August 30, 2011
by Yoshio Mimura, Kobe, Japan

7037

70372 = 65 + 135 + 295 + 315.

Page of Squares : First Upload March 31, 2008 ; Last Revised March 31, 2008
by Yoshio Mimura, Kobe, Japan

7038

70382 = 114 + 294 + 494 + 814.

Page of Squares : First Upload March 31, 2008 ; Last Revised March 31, 2008
by Yoshio Mimura, Kobe, Japan

7039

70392 = 49547521, and 4 - 9 * 54 + 7521 = 7039.

70395 = 17280441177370659199 :
172 + 22 + 82 + 02 + 442 + 112 + 72 + 72 + 32 + 72 + 02 + 652 + 92 + 12 + 92 + 92 = 7039.

Page of Squares : First Upload March 31, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

7041

70412 = 233 + 513 + 3673 = 1863 + 1963 + 3293.

Page of Squares : First Upload March 31, 2008 ; Last Revised March 31, 2008
by Yoshio Mimura, Kobe, Japan

7044

70443 = 349508741184, and 32 + 492 + 502 + 82 + 72 + 412 + 182 + 42 = 7044.

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

7045

70452 = 49632025, and 49 = 72, 632025 = 7952.

Page of Squares : First Upload March 31, 2008 ; Last Revised March 31, 2008
by Yoshio Mimura, Kobe, Japan

7047

70472 = 14 + 344 + 424 + 824.

Page of Squares : First Upload March 31, 2008 ; Last Revised March 31, 2008
by Yoshio Mimura, Kobe, Japan

7048

70482 = 2003 + 2563 + 2923.

Page of Squares : First Upload March 31, 2008 ; Last Revised March 31, 2008
by Yoshio Mimura, Kobe, Japan

7049

70493 = 350253538649, and 32 + 502 + 252 + 32 + 52 + 382 + 62 + 492 = 7049.

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

7050

6204k + 7050k + 52593k + 113082k are squares for k = 1,2,3 (4232, 1250672, 399011672).

Page of Squares : First Upload July 5, 2011 ; Last Revised July 5, 2011
by Yoshio Mimura, Kobe, Japan

7053

70532 = 1723 + 2493 + 3083.

Page of Squares : First Upload March 31, 2008 ; Last Revised March 31, 2008
by Yoshio Mimura, Kobe, Japan

7055

70555 = 17477732594525159375 :
12 + 72 + 42 + 72 + 72 + 732 + 252 + 92 + 42 + 52 + 252 + 12 + 52 + 92 + 32 + 72 + 52 = 7055.

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

7056

The square of 84.

70562 = 49787136, and
4 * 9 * 7 * 8 * 7 * 1 * 3 / 6 = 49 * 7 * 8 / 7 * 1 * 3 * 6 = 49 / 7 * 8 * 7 * 1 * 3 * 6 = 7056.

Komachi equations:
70562 = 122 / 32 * 42 * 562 * 72 / 82 * 92,
70562 = 14 * 24 / 34 / 44 * 5674 * 84 / 94,
70562 = 94 * 84 * 74 * 64 / 544 * 34 / 24 */ 14 = 984 / 74 / 64 * 544 / 34 * 24 */ 14,
70562 = 94 / 84 * 74 / 64 * 54 * 44 * 324 / 104.

70562 = (4 + 5 + 6 + ... + 24)2 + (25 + 26 + 27 + ... + 45)2 + (46 + 47 + 48 + ... + 66)2 + ... + (172 + 173 + 174 + ... + 192)2.

70562 = 123 + 2283 + 3363 = 243 + 2543 + 3223.

Page of Squares : First Upload March 31, 2008 ; Last Revised November 5, 2010
by Yoshio Mimura, Kobe, Japan

7057

70572 = 573 + 573 + 3673.

Page of Squares : First Upload March 31, 2008 ; Last Revised March 31, 2008
by Yoshio Mimura, Kobe, Japan

7059

70592 = 49829481, and 4 * 98 * 2 * 9 - 4 + 8 - 1 = 49 * 8 * 2 * 9 - 4 + 8 - 1 = 7059.

Page of Squares : First Upload March 31, 2008 ; Last Revised March 31, 2008
by Yoshio Mimura, Kobe, Japan

7060

70602 = 49843600, and 4 + 98 * 4 * 3 * 6 + 0 + 0 = 4 + 98 * 4 * 3 * 6 + 0 * 0 = 7060.

70602 = 93 + 1913 + 3503.

Page of Squares : First Upload March 31, 2008 ; Last Revised March 31, 2008
by Yoshio Mimura, Kobe, Japan

7061

70612 = 49857721, and 42 + 92 + 82 + 52 + 72 + 72 + 22 + 12 = 172.

Page of Squares : First Upload March 31, 2008 ; Last Revised March 31, 2008
by Yoshio Mimura, Kobe, Japan

7062

70625 = 17564612218807892832 :
172 + 52 + 642 + 62 + 12 + 222 + 12 + 82 + 82 + 02 + 72 + 82 + 92 + 282 + 322 = 7062.

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

7064

70642 = 43 + 403 + 3683 = 1763 + 2623 + 2983 = 1863 + 1873 + 3333.

Page of Squares : First Upload March 31, 2008 ; Last Revised March 31, 2008
by Yoshio Mimura, Kobe, Japan

7065

The square root of 7065 is 84.05355...., and 84 = 02 + 52 + 32 + 52 + 52.

70652 = 663 + 1783 + 3533.

Page of Squares : First Upload March 31, 2008 ; Last Revised March 31, 2008
by Yoshio Mimura, Kobe, Japan

7066

70665 = 17614412618408092576 :
172 + 62 + 12 + 42 + 42 + 12 + 262 + 12 + 82 + 42 + 02 + 82 + 02 + 92 + 22 + 52 + 762 = 7066.

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

7068

70682 = (112 + 3)(152 + 3)(422 + 3) = (32 + 3)(42 + 3)(112 + 3)(422 + 3).

70682 = 144 + 164 + 164 + 844.

7068 = (12 + 22 + 32 + ... + 10072) / (12 + 22 + 32 + ... + 522).

Page of Squares : First Upload March 31, 2008 ; Last Revised January 11, 2014
by Yoshio Mimura, Kobe, Japan

7069

70695 = 17651836994323266349 :
12 + 762 + 52 + 182 + 32 + 62 + 92 + 92 + 42 + 32 + 232 + 22 + 62 + 62 + 32 + 42 + 92 = 7069.

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

7070

70702± 3 are primes.

70702 = (12 + 6)(142 + 6)(1882 + 6).

Page of Squares : First Upload January 11, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

7072

4420k + 7072k + 11713k + 25636k are squares for k = 1,2,3 (2212, 293932, 43468492).

Page of Squares : First Upload July 5, 2011 ; Last Revised July 5, 2011
by Yoshio Mimura, Kobe, Japan

7074

70742 = (22 + 2)(282 + 2)(1032 + 2).

70742 = 363 + 1893 + 3513.

Page of Squares : First Upload March 31, 2008 ; Last Revised January 11, 2014
by Yoshio Mimura, Kobe, Japan

7077

70772± 2 are primes.

70775 = 17751946404233219157 :
172 + 72 + 512 + 92 + 462 + 42 + 02 + 42 + 232 + 322 + 12 + 92 + 152 + 72 = 7077.

Page of Squares : First Upload December 8, 2008 ; Last Revised January 11, 2014
by Yoshio Mimura, Kobe, Japan

7079

70792 = 893 + 2343 + 3323.

Page of Squares : First Upload March 31, 2008 ; Last Revised March 31, 2008
by Yoshio Mimura, Kobe, Japan

7082

70825 = 17814745076453558432 :
12 + 72 + 82 + 12 + 42 + 72 + 452 + 02 + 72 + 62 + 42 + 532 + 52 + 52 + 82 + 432 + 22 = 7082.

70822 = 30 + 32 + 35 + 37 + 39 + 311 + 312 + 313 + 314 + 316.

Page of Squares : First Upload December 8, 2008 ; Last Revised August 30, 2011
by Yoshio Mimura, Kobe, Japan

7084

70842 = (42 + 7)(352 + 7)(422 + 7).

70842 = 1263 + 1323 + 3583.

1265k + 7084k + 16192k + 39468k are squares for k = 1,2,3 (2532, 432632, 81291432).

Page of Squares : First Upload March 31, 2008 ; Last Revised January 11, 2014
by Yoshio Mimura, Kobe, Japan

7092

70922 = (83 + 84 + 85)2 + (86 + 87 + 88)2 + (89 + 90 + 91)2 + ... + (368 + 369 + 370)2.

Page of Squares : First Upload March 31, 2008 ; Last Revised March 31, 2008
by Yoshio Mimura, Kobe, Japan

7098

70982 = (22 + 3)(32 + 3)(62 + 3)(1242 + 3) = (62 + 3)(92 + 3)(1242 + 3).

Page of Squares : First Upload January 11, 2014 ; Last Revised January 11, 2014
by Yoshio Mimura, Kobe, Japan