6900
69005 = 15640313490000000000 :
152 + 642 + 02 + 32 + 132 + 492 + 02 + 02 + 02 + 02 + 02 + 02 + 02 + 02 + 02 + 02 = 6900.
830k + 2010k + 4570k + 4690k are squares for k = 1,2,3 (1102, 69002, 4553002).
Page of Squares : First Upload December 8, 2008 ; Last Revised July 5, 2011by Yoshio Mimura, Kobe, Japan
6901
69012 = 47623801, a square with different digits.
69014 = 2268026421687601,
and 22 + 22 + 62 + 82 + 02 + 262 + 42 + 22 + 162 + 82 + 762 + 02 + 12 = 6901,
and 22 + 262 + 82 + 02 + 22 + 62 + 42 + 22 + 162 + 82 + 762 + 02 + 12 = 6901.
by Yoshio Mimura, Kobe, Japan
6902
69022 = 993 + 2523 + 3133.
938k + 1274k + 3430k + 6902k are squares for k = 1,2,3 (1122, 78682, 6099522).
Page of Squares : First Upload March 24, 2008 ; Last Revised July 5, 2011by Yoshio Mimura, Kobe, Japan
6904
69042 = 1323 + 2163 + 3283.
Page of Squares : First Upload March 24, 2008 ; Last Revised March 24, 2008by Yoshio Mimura, Kobe, Japan
6906
69062 = 47692836, a zigzag square.
69062 = 47692836, and 42 + 72 + 692 + 282 + 362.
Page of Squares : First Upload March 24, 2008 ; Last Revised November 25, 2008by Yoshio Mimura, Kobe, Japan
6908
69082 = 6572 + 6582 + 6592 + 6602 + ... + 7522.
69082 = 233 + 1883 + 3453 = 2183 + 2183 + 3003.
Page of Squares : First Upload March 24, 2008 ; Last Revised March 24, 2008by Yoshio Mimura, Kobe, Japan
6909
69092 = 47734281, and 47 * 7 * 3 / 4 * 28 * 1 = 6909.
69092 = 493 + 1683 + 3503 = 813 + 2623 + 3083.
Komachi equation: 69092 = 9872 * 62 / 542 * 32 * 212.
Page of Squares : First Upload March 24, 2008 ; Last Revised November 2, 2010by Yoshio Mimura, Kobe, Japan
6911
69114 = 2281201097610241,
and 22 + 282 + 122 + 02 + 12 + 02 + 92 + 762 + 102 + 22 + 42 + 12 = 6911,
and 22 + 282 + 122 + 02 + 102 + 92 + 762 + 12 + 02 + 22 + 42 + 12 = 6911.
by Yoshio Mimura, Kobe, Japan
6912
69122 = 47775744, a square with just 3 kinds of digits.
69122 = 2883 + 2883.
Page of Squares : First Upload March 24, 2008 ; Last Revised March 24, 2008by Yoshio Mimura, Kobe, Japan
6913
69134 = 2283842905205761,
and 22 + 282 + 382 + 42 + 292 + 02 + 52 + 22 + 02 + 52 + 72 + 612 = 6913.
by Yoshio Mimura, Kobe, Japan
6914
69144 = 2285164669132816,
and 22 + 22 + 82 + 52 + 12 + 62 + 42 + 62 + 62 + 92 + 12 + 32 + 22 + 812 + 62 = 6914.
by Yoshio Mimura, Kobe, Japan
6915
69152 = 1483 + 1523 + 3453.
Page of Squares : First Upload March 24, 2008 ; Last Revised March 24, 2008by Yoshio Mimura, Kobe, Japan
6916
69162 = 47831056, a square with different digits.
69162 = (12 + 3)(22 + 3)(13072 + 3) = (12 + 3)(42 + 3)(72 + 3)(1102 + 3)
= (22 + 3)(192 + 3)(1372 + 3) = (52 + 3)(13072 + 3).
6916 = (12 + 22 + 32 + ... + 1042) / (12 + 22 + 32 + 42 + 52).
69165 = 15822493393407640576 :
12 + 52 + 82 + 22 + 242 + 92 + 332 + 92 + 32 + 42 + 02 + 72 + 62 + 402 + 572 + 62
= 12 + 52 + 82 + 22 + 242 + 92 + 332 + 92 + 32 + 402 + 72 + 62 + 42 + 02 + 572 + 62 = 6916.
by Yoshio Mimura, Kobe, Japan
6917
69175 = 15833935751472194357 :
12 + 52 + 82 + 32 + 32 + 92 + 352 + 72 + 52 + 142 + 72 + 22 + 12 + 92 + 432 + 572 = 6917.
by Yoshio Mimura, Kobe, Japan
6918
1 / 6918 = 0.000144550448106, 12 + 442 + 52 + 502 + 42 + 482 + 102 + 62 = 6918.
Page of Squares : First Upload March 24, 2008 ; Last Revised March 24, 2008by Yoshio Mimura, Kobe, Japan
6920
69202 = (22 + 4)(132 + 4)(1862 + 4).
69202 = 43 + 2803 + 2963.
69205 = 15868302550323200000 :
12 + 582 + 62 + 82 + 302 + 22 + 52 + 502 + 32 + 22 + 32 + 22 + 02 + 02 + 02 + 02 + 02 = 6920.
by Yoshio Mimura, Kobe, Japan
6921
1 / N = 0.0001444...., and 1444 = 382 for N = 6921, 6922, ..., 6925.
Page of Squares : First Upload March 24, 2008 ; Last Revised March 24, 2008by Yoshio Mimura, Kobe, Japan
6924
69242 = 13 + 2723 + 3033 = 63 + 2543 + 3163 = 163 + 2313 + 3293 = 443 + 1863 + 3463.
Page of Squares : First Upload March 24, 2008 ; Last Revised March 24, 2008by Yoshio Mimura, Kobe, Japan
6925
69252 = 47955625, and 4 * 7 * 9 * 5 * 5 + 625 = 4 - 79 + 5 * 56 * 25 = 6925.
69252 = 753 + 2153 + 3353.
Page of Squares : First Upload March 24, 2008 ; Last Revised March 24, 2008by Yoshio Mimura, Kobe, Japan
6926
69265 = 15937215167551153376 :
12 + 52 + 92 + 32 + 72 + 212 + 52 + 162 + 72 + 52 + 52 + 112 + 52 + 32 + 32 + 762 = 6926.
by Yoshio Mimura, Kobe, Japan
6928
69282 = (76 + 77 + 78 + 79)2 + (80 + 81 + 82 + 83)2 + (84 + 85 + 86 + 87)2 + ... + (328 + 329 + 330 + 331)2.
69282 = 84 + 564 + 644 + 684.
Page of Squares : First Upload March 24, 2008 ; Last Revised March 24, 2008by Yoshio Mimura, Kobe, Japan
6929
69292 = 1693 + 2343 + 3123.
Page of Squares : First Upload March 24, 2008 ; Last Revised March 24, 2008by Yoshio Mimura, Kobe, Japan
6930
The integral triangle of sides 14841, 21809, 36250 (or 9801, 480250, 490049)(or 99, 970249, 970250) has square area 69302.
69302 = (32 + 6)(62 + 6)(152 + 6)(182 + 6).
69302 = 1 + 2 + 3 + ... + 9800 = 98002 - 97992 + 97982 - 97972 + ... - 12.
Page of Squares : First Upload March 24, 2008 ; Last Revised January 11, 2014by Yoshio Mimura, Kobe, Japan
6932
69322 = 48052624, a zigzag square.
Page of Squares : First Upload March 24, 2008 ; Last Revised March 24, 2008by Yoshio Mimura, Kobe, Japan
6933
69332 = 1123 + 2333 + 3243.
Page of Squares : First Upload March 24, 2008 ; Last Revised March 24, 2008by Yoshio Mimura, Kobe, Japan
6934
69344 = 2311720633086736,
and 22 + 312 + 12 + 72 + 202 + 62 + 32 + 32 + 02 + 82 + 62 + 732 + 62 = 6934.
69345 = 16029470869823427424 :
12 + 602 + 22 + 92 + 472 + 02 + 82 + 62 + 92 + 82 + 22 + 32 + 42 + 272 + 42 + 22 + 42 = 6934.
by Yoshio Mimura, Kobe, Japan
6935
69352 = 1533 + 2723 + 2903.
Page of Squares : First Upload March 24, 2008 ; Last Revised March 24, 2008by Yoshio Mimura, Kobe, Japan
6936
852 + 6936 = 1192, 852 - 6936 = 172.
69362 = 163 + 1443 + 3563 = 163+ 2303 + 3303 = 683 + 2043 + 3403.
Page of Squares : First Upload March 24, 2008 ; Last Revised August 5, 2011by Yoshio Mimura, Kobe, Japan
6937
69372 = 48121969, a zigzag square.
69372 = 264 + 264 + 614 + 764 = 524 + 524 + 594 + 684.
Page of Squares : First Upload March 24, 2008 ; Last Revised March 24, 2008by Yoshio Mimura, Kobe, Japan
6945
69452 = 703 + 2733 + 3023.
Page of Squares : First Upload March 24, 2008 ; Last Revised March 24, 2008by Yoshio Mimura, Kobe, Japan
6946
69462 = 48246916, and 4 * 8 + 2 - 4 + 6916 = 6946.
Page of Squares : First Upload March 24, 2008 ; Last Revised March 24, 2008by Yoshio Mimura, Kobe, Japan
6947
69472 = 48260809, a zigzag square.
Page of Squares : First Upload March 24, 2008 ; Last Revised March 24, 2008by Yoshio Mimura, Kobe, Japan
6948
69482 = 48274704, a zigzag square.
69482 + 40782 = 64904788 (a mosaic square).
1 / 6948 = 0.00014392630972, 12 + 42 + 32 + 92 + 262 + 302 + 92 + 722 = 6948.
Page of Squares : First Upload March 24, 2008 ; Last Revised March 24, 2008by Yoshio Mimura, Kobe, Japan
6952
69522 = (12 + 7)(92 + 7)(2622 + 7).
Page of Squares : First Upload January 11, 2014 ; Last Revised January 11, 2014by Yoshio Mimura, Kobe, Japan
6953
69532 = 833 + 2013 + 3413.
Page of Squares : First Upload March 24, 2008 ; Last Revised March 24, 2008by Yoshio Mimura, Kobe, Japan
6956
69562 = 48385936, a zigzag square.
Page of Squares : First Upload March 24, 2008 ; Last Revised March 24, 2008by Yoshio Mimura, Kobe, Japan
6957
69572± 2 are primes.
69572 = 48399849, and 48 * 3 + 9 + 9 * 84 * 9 = 48 * 3 + 9 * 9 * 84 + 9 = 6957.
Page of Squares : First Upload March 24, 2008 ; Last Revised March 24, 2008by Yoshio Mimura, Kobe, Japan
6958
69582 = 33 + 573 + 3643.
2282k + 3010k + 3626k + 6958k are squares for k = 1,2,3 (1262, 87082, 6509162).
Page of Squares : First Upload March 24, 2008 ; Last Revised July 5, 2011by Yoshio Mimura, Kobe, Japan
6960
609k + 4524k + 6960k + 8932k are squares for k = 1,2,3 (1452, 122092, 10689112).
Page of Squares : First Upload July 5, 2011 ; Last Revised July 5, 2011by Yoshio Mimura, Kobe, Japan
6961
69612 = 48455521, and 4 * 8 * 45 + 5521 = 6961.
Page of Squares : First Upload March 24, 2008 ; Last Revised March 24, 2008by Yoshio Mimura, Kobe, Japan
6962
69622 = 594 + 594 + 594 + 594.
Page of Squares : First Upload March 24, 2008 ; Last Revised March 24, 2008by Yoshio Mimura, Kobe, Japan
6963
1 / 6963 = 0.00014361625736, 12 + 42 + 362 + 162 + 22 + 52 + 732 + 62 = 6963.
69632 = 48483369, and 48 * 48 * 3 - 3 + 6 * 9 = 6963.
Page of Squares : First Upload March 24, 2008 ; Last Revised March 24, 2008by Yoshio Mimura, Kobe, Japan
6964
Loop of length 14 by the function f(N) = ... + c2 + b2 + a2 where N = ... + 1002c + 100b + a:
6964 - 8857 - 10993 - 8731 - ... - 4250 - 4264 - 5860 - 6964
(Note f(6964) = 692 + 642 = 8857, f(8857) = 882 + 572 = 10993, etc. See 1946)
1 / 6964 = 0.00014359563469, 142 + 32 + 592 + 562 + 32 + 42 + 62 + 92 = 6964.
Page of Squares : First Upload March 24, 2008 ; Last Revised October 9, 2008by Yoshio Mimura, Kobe, Japan
6965
(69652 + 7) = (22 + 7)(42 + 7)(52 + 7)(72 + 7)(102 + 7).
69655 = 16391005793719353125 :
162 + 32 + 92 + 12 + 02 + 02 + 52 + 792 + 32 + 72 + 12 + 92 + 32 + 52 + 32 + 122 + 52 = 6965.
by Yoshio Mimura, Kobe, Japan
6966
69662 = (12 + 2)(42 + 2)(162 + 2)(592 + 2) = (22 + 5)(72 + 5)(92 + 5)(342 + 5).
69662 = 48525156, and 42 + 82 + 52 + 22 + 52 + 12 + 52 + 62 = 142.
69662 = 363 + 1953 + 3453.
Page of Squares : First Upload March 24, 2008 ; Last Revised January 11, 2014by Yoshio Mimura, Kobe, Japan
6967
69672 = 124 + 214 + 424 + 824.
69672 = 30 + 34 + 36 + 311 + 312 + 314 + 316.
Page of Squares : First Upload March 24, 2008 ; Last Revised August 30, 2011by Yoshio Mimura, Kobe, Japan
6968
69682 = (12 + 3)(72 + 3)(82 + 3)(592 + 3).
Page of Squares : First Upload January 11, 2014 ; Last Revised January 11, 2014by Yoshio Mimura, Kobe, Japan
6970
69702 = (12 + 1)(132 + 1)(3782 + 1) = (12 + 1)(32 + 1)(42 + 1)(3782 + 1)
= (12 + 1)(42 + 1)(92 + 1)(1322 + 1) = (92 + 4)(7562 + 4).
by Yoshio Mimura, Kobe, Japan
6972
69722 = (65 + 66 + 67 + ... + 92)2 + (93 + 94 + 95 + ... + 120)2 + (121 + 122 + 123 + ... + 148)2 + ... + (149 + 150 + 151 + ... + 176)2.
69722 = 213 + 2833 + 2963.
Page of Squares : First Upload March 24, 2008 ; Last Revised March 24, 2008by Yoshio Mimura, Kobe, Japan
6973
69732 = 48622729, and 4 * 8 * 62 / 2 * 7 + 29 = 6973.
Page of Squares : First Upload March 24, 2008 ; Last Revised March 24, 2008by Yoshio Mimura, Kobe, Japan
6974
1265k + 1529k + 3817k + 5489k are squares for k = 1,2,3 (1102, 69742, 4760142).
Page of Squares : First Upload July 5, 2011 ; Last Revised July 5, 2011by Yoshio Mimura, Kobe, Japan
6977
69775 = 16532693517957998657 :
162 + 52 + 32 + 262 + 92 + 352 + 12 + 72 + 92 + 52 + 72 + 92 + 92 + 82 + 652 + 72 = 6977.
by Yoshio Mimura, Kobe, Japan
6983
69832 = 48762289, and 4 * 876 * 2 - 2 * 8 - 9 = 48 + 7 * 62 * 2 * 8 - 9 = 6983.
69834 = 2377760828519521,
and 22 + 32 + 72 + 72 + 72 + 602 + 82 + 22 + 82 + 52 + 192 + 522 + 12 = 6983.
by Yoshio Mimura, Kobe, Japan
6984
The square root of 6984 is 83.5703...., and 83 = 52 + 72 + 02 + 32.
69845 = 16615796075252711424 :
12 + 62 + 62 + 12 + 572 + 92 + 62 + 02 + 72 + 52 + 22 + 522 + 72 + 112 + 42 + 242
= 12 + 62 + 62 + 12 + 572 + 92 + 62 + 02 + 72 + 522 + 52 + 22 + 72 + 112 + 42 + 242
= 162 + 62 + 152 + 72 + 92 + 62 + 02 + 752 + 22 + 52 + 22 + 72 + 12 + 12 + 42 + 242
= 12 + 62 + 62 + 152 + 72 + 92 + 62 + 02 + 752 + 252 + 22 + 72 + 12 + 142 + 22 + 42 = 6984.
by Yoshio Mimura, Kobe, Japan
6986
69862 = 2912 + 2932 + 2952 + 2972 + ... + 6812.
Page of Squares : First Upload March 24, 2008 ; Last Revised March 24, 2008by Yoshio Mimura, Kobe, Japan
6988
69882 = 48832144, and 4 + 8 + 83 * 21 * 4 + 4 = 6988.
69885 = 16663433074005511168 :
12 + 62 + 62 + 632 + 42 + 32 + 302 + 72 + 402 + 02 + 52 + 52 + 12 + 12 + 162 + 82
= 12 + 62 + 62 + 632 + 42 + 32 + 32 + 02 + 72 + 42 + 02 + 02 + 52 + 512 + 112 + 62 + 82
= 162 + 62 + 632 + 42 + 32 + 302 + 72 + 402 + 02 + 52 + 52 + 12 + 12 + 12 + 62 + 82 = 6988.
by Yoshio Mimura, Kobe, Japan
6992
69922 = 48888064, a square with even digits.
69922 = 48888064, and 42 + 82 + 82 + 82 + 82 + 02 + 62 + 42 = 182.
69922 = 183 + 1743 + 3523 = 443 + 2263 + 3343 = 783 + 1113 + 3613 = 1583 + 1783 + 3403.
Page of Squares : First Upload March 24, 2008 ; Last Revised March 24, 2008by Yoshio Mimura, Kobe, Japan
6993
69935 = 16723132902014018193 :
162 + 722 + 32 + 132 + 22 + 92 + 02 + 202 + 142 + 02 + 182 + 192 + 32 = 6993.
by Yoshio Mimura, Kobe, Japan
6994
130k + 1794k + 6994k + 7982k are squares for k = 1,2,3 (1302, 107642, 9254442).
Page of Squares : First Upload July 5, 2011 ; Last Revised July 5, 2011by Yoshio Mimura, Kobe, Japan
6995
The square root of 6995 is 83.63611...., and 83 = 62 + 32 + 62 + 12 + 12.
Page of Squares : First Upload March 24, 2008 ; Last Revised March 24, 2008by Yoshio Mimura, Kobe, Japan
6999
69992 = 13 + 2253 + 3353.
Page of Squares : First Upload March 24, 2008 ; Last Revised March 24, 2008by Yoshio Mimura, Kobe, Japan