logo
1000 - 1099

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, 2011
by 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.

Page of Squares : First Upload March 24, 2008 ; Last Revised December 1, 2008
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, 2011
by Yoshio Mimura, Kobe, Japan

6904

69042 = 1323 + 2163 + 3283.

Page of Squares : First Upload March 24, 2008 ; Last Revised March 24, 2008
by 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, 2008
by 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, 2008
by 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, 2010
by 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.

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

6913

69134 = 2283842905205761,
and 22 + 282 + 382 + 42 + 292 + 02 + 52 + 22 + 02 + 52 + 72 + 612 = 6913.

Page of Squares : First Upload December 1, 2008 ; Last Revised December 1, 2008
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.

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

6915

69152 = 1483 + 1523 + 3453.

Page of Squares : First Upload March 24, 2008 ; Last Revised March 24, 2008
by 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.

Page of Squares : First Upload March 24, 2008 ; Last Revised January 11, 2014
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.

Page of Squares : First Upload December 8, 2008 ; Last Revised December 8, 2008
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, 2008
by 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.

Page of Squares : First Upload March 24, 2008 ; Last Revised January 11, 2014
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, 2008
by 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, 2008
by 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, 2008
by Yoshio Mimura, Kobe, Japan

6926

69265 = 15937215167551153376 :
12 + 52 + 92 + 32 + 72 + 212 + 52 + 162 + 72 + 52 + 52 + 112 + 52 + 32 + 32 + 762 = 6926.

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

6929

69292 = 1693 + 2343 + 3123.

Page of Squares : First Upload March 24, 2008 ; Last Revised March 24, 2008
by 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, 2014
by Yoshio Mimura, Kobe, Japan

6932

69322 = 48052624, a zigzag square.

Page of Squares : First Upload March 24, 2008 ; Last Revised March 24, 2008
by Yoshio Mimura, Kobe, Japan

6933

69332 = 1123 + 2333 + 3243.

Page of Squares : First Upload March 24, 2008 ; Last Revised March 24, 2008
by 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.

Page of Squares : First Upload December 1, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

6935

69352 = 1533 + 2723 + 2903.

Page of Squares : First Upload March 24, 2008 ; Last Revised March 24, 2008
by 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, 2011
by 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, 2008
by Yoshio Mimura, Kobe, Japan

6945

69452 = 703 + 2733 + 3023.

Page of Squares : First Upload March 24, 2008 ; Last Revised March 24, 2008
by 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, 2008
by Yoshio Mimura, Kobe, Japan

6947

69472 = 48260809, a zigzag square.

Page of Squares : First Upload March 24, 2008 ; Last Revised March 24, 2008
by 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, 2008
by Yoshio Mimura, Kobe, Japan

6952

69522 = (12 + 7)(92 + 7)(2622 + 7).

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

6953

69532 = 833 + 2013 + 3413.

Page of Squares : First Upload March 24, 2008 ; Last Revised March 24, 2008
by Yoshio Mimura, Kobe, Japan

6956

69562 = 48385936, a zigzag square.

Page of Squares : First Upload March 24, 2008 ; Last Revised March 24, 2008
by 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, 2008
by 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, 2011
by 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, 2011
by 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, 2008
by Yoshio Mimura, Kobe, Japan

6962

69622 = 594 + 594 + 594 + 594.

Page of Squares : First Upload March 24, 2008 ; Last Revised March 24, 2008
by 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, 2008
by 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, 2008
by 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.

Page of Squares : First Upload March 24, 2008 ; Last Revised December 8, 2008
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, 2014
by 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, 2011
by 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, 2014
by 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).

Page of Squares : First Upload November 2, 2013 ; Last Revised January 11, 2014
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, 2008
by 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, 2008
by 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, 2011
by Yoshio Mimura, Kobe, Japan

6977

69775 = 16532693517957998657 :
162 + 52 + 32 + 262 + 92 + 352 + 12 + 72 + 92 + 52 + 72 + 92 + 92 + 82 + 652 + 72 = 6977.

Page of Squares : First Upload December 8, 2008 ; Last Revised December 8, 2008
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.

Page of Squares : First Upload March 24, 2008 ; Last Revised December 1, 2008
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.

Page of Squares : First Upload March 24, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

6986

69862 = 2912 + 2932 + 2952 + 2972 + ... + 6812.

Page of Squares : First Upload March 24, 2008 ; Last Revised March 24, 2008
by 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.

Page of Squares : First Upload March 24, 2008 ; Last Revised December 8, 2008
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, 2008
by Yoshio Mimura, Kobe, Japan

6993

69935 = 16723132902014018193 :
162 + 722 + 32 + 132 + 22 + 92 + 02 + 202 + 142 + 02 + 182 + 192 + 32 = 6993.

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

6999

69992 = 13 + 2253 + 3353.

Page of Squares : First Upload March 24, 2008 ; Last Revised March 24, 2008
by Yoshio Mimura, Kobe, Japan