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8900 - 8999

8900

89002 = 1353 + 2703 + 3853.

Page of Squares : First Upload August 18, 2008 ; Last Revised August 18, 2008
by Yoshio Mimura, Kobe, Japan

8901

89012 = 79227801, and 7 * 9 * 22 * 7 - 801 = 8901.

138k + 713k + 5152k + 7222k are squares for k = 1,2,3 (1152, 89012, 7167952).

Page of Squares : First Upload August 18, 2008 ; Last Revised July 15, 2011
by Yoshio Mimura, Kobe, Japan

8903

89032 = 79263409, a zigzag square.

89032 = 64 + 64 + 334 + 944.

Page of Squares : First Upload August 18, 2008 ; Last Revised August 18, 2008
by Yoshio Mimura, Kobe, Japan

8904

89042 = 79281216, a zigzag square.

Page of Squares : First Upload August 18, 2008 ; Last Revised August 18, 2008
by Yoshio Mimura, Kobe, Japan

8905

89052 = 79299025, and 792 + 9 * 902 - 5 = 8905.

Page of Squares : First Upload August 18, 2008 ; Last Revised August 18, 2008
by Yoshio Mimura, Kobe, Japan

8907

The square root of 8907 is 94.376...., and 94 = 32 + 72 + 62.

Page of Squares : First Upload August 18, 2008 ; Last Revised August 18, 2008
by Yoshio Mimura, Kobe, Japan

8910

89102 = 453 + 3033 + 3723 = 493 + 2673 + 3923 = 1093 + 1343 + 4233 = 1353 + 3333 + 3423.

The square root of 8910 is 94.392...., and 94 = 32 + 92 + 22.

89102 = 79388100, and 7 + 93 + 8810 + 0 = 8910.

Page of Squares : First Upload August 18, 2008 ; Last Revised August 18, 2008
by Yoshio Mimura, Kobe, Japan

8918

89182 = (172 + 173 + 174 + 175 + 176 + 177 + 178)2 + (179 + 180 + 181 + 182 + 183 + 184 + 185)2 + (186 + 187 + 188 + 189 + 190 + 191 + 192)2 + ... + (333 + 334 + 335 + 336 + 337 + 338 + 339)2.

89185 = 56407563382760521568, and
52 + 62 + 402 + 72 + 52 + 62 + 332 + 82 + 22 + 72 + 62 + 02 + 522 + 12 + 562 + 82
= 52 + 62 + 402 + 752 + 62 + 332 + 82 + 22 + 72 + 62 + 02 + 52 + 22 + 152 + 62 + 82
= 52 + 62 + 402 + 72 + 562 + 332 + 82 + 22 + 72 + 62 + 02 + 522 + 12 + 52 + 62 + 82
= 562 + 402 + 72 + 52 + 62 + 332 + 82 + 22 + 72 + 62 + 02 + 522 + 12 + 52 + 62 + 82 = 8918.

Page of Squares : First Upload August 18, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

8921

89212 = 79584241, and 72 + 92 + 52 + 82 + 42 + 22 + 42 + 12 = 162.

89215 = 56502504278086588601, and
562 + 52 + 02 + 22 + 52 + 02 + 422 + 72 + 82 + 02 + 82 + 62 + 52 + 82 + 82 + 602 + 12
= 52 + 62 + 52 + 02 + 22 + 502 + 422 + 72 + 82 + 02 + 82 + 652 + 82 + 82 + 62 + 02 + 12
= 52 + 62 + 502 + 22 + 52 + 02 + 422 + 72 + 82 + 02 + 82 + 652 + 82 + 82 + 62 + 02 + 12
= 52 + 652 + 02 + 22 + 502 + 422 + 72 + 82 + 02 + 82 + 62 + 52 + 82 + 82 + 62 + 02 + 12 = 8921.

Page of Squares : First Upload August 18, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

8923

89232 = 79619929, and 79 * 6 * 19 - 92 + 9 = 8923.

Page of Squares : First Upload August 18, 2008 ; Last Revised August 18, 2008
by Yoshio Mimura, Kobe, Japan

8925

89252 = (123 + 124 + 125 + 126 + 127)2 + (128 + 129 + 130 + 131 + 132)2 + (133 + 134 + 135 + 136 + 137)2 + ... + (363 + 364 + 365 + 366 + 367)2.

Page of Squares : First Upload August 18, 2008 ; Last Revised August 18, 2008
by Yoshio Mimura, Kobe, Japan

8927

89272 = 79691329, a zigzag square.

89272 = 903 + 2413 + 4023 = 44 + 234 + 344 + 944.

Page of Squares : First Upload August 18, 2008 ; Last Revised August 18, 2008
by Yoshio Mimura, Kobe, Japan

8929

89295 = 56756305123811415649, and
52 + 672 + 52 + 62 + 302 + 52 + 122 + 382 + 12 + 12 + 412 + 52 + 62 + 42 + 92
= 52 + 672 + 52 + 62 + 32 + 02 + 512 + 22 + 382 + 112 + 42 + 12 + 52 + 62 + 42 + 92 = 8929.

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

8932

89322 = 79780624, a zigzag square.

89322 = (22 + 7)(142 + 7)(1892 + 7).

609k + 4524k + 6960k + 8932k are squares for k = 1,2,3 (1452, 122092, 10689112).

Page of Squares : First Upload August 18, 2008 ; Last Revised January 11, 2014
by Yoshio Mimura, Kobe, Japan

8936

89362 = 2803 + 2883 + 3243.

89364 = 6376357235593216, and
62 + 32 + 72 + 632 + 52 + 72 + 22 + 32 + 52 + 592 + 322 + 162
= 632 + 72 + 62 + 32 + 52 + 72 + 22 + 32 + 52 + 592 + 322 + 162.

89365 = 56979128257260978176, and
52 + 692 + 72 + 92 + 122 + 82 + 22 + 572 + 22 + 62 + 02 + 92 + 72 + 82 + 172 + 62 = 8936.

Page of Squares : First Upload August 18, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

8937

89372 = 79869969, a square every digit of which is greater than 5.

89372 = 274 + 484 + 784 + 784.

Page of Squares : First Upload August 18, 2008 ; Last Revised September 7, 2013
by Yoshio Mimura, Kobe, Japan

8938

89382 = 79887844, and 7 + 9 + 8878 + 44 = 8938 .

Page of Squares : First Upload August 18, 2008 ; Last Revised August 18, 2008
by Yoshio Mimura, Kobe, Japan

8940

89402 = 343 + 1143 + 4283.

Page of Squares : First Upload August 18, 2008 ; Last Revised August 18, 2008
by Yoshio Mimura, Kobe, Japan

8942

89422 = 34 + 74 + 694 + 874.

Page of Squares : First Upload August 18, 2008 ; Last Revised August 18, 2008
by Yoshio Mimura, Kobe, Japan

8943

89432 = 163 + 3293 + 3543 = 2173 + 2463 + 3803.

Page of Squares : First Upload August 18, 2008 ; Last Revised August 18, 2008
by Yoshio Mimura, Kobe, Japan

8944

89442 = 79995136, a square with odd digits except the last digit 6.

89442 = 79995136, and 7 + 9 * 995 - 1 * 3 * 6 = 7 + 9 * 995 * 1 - 3 * 6 = 8944.

Page of Squares : First Upload August 18, 2008 ; Last Revised August 24, 2013
by Yoshio Mimura, Kobe, Japan

8945

89452 = 2563 + 2683 + 3533.

Page of Squares : First Upload August 18, 2008 ; Last Revised August 18, 2008
by Yoshio Mimura, Kobe, Japan

8946

89462 = 2283 + 2733 + 3633.

Page of Squares : First Upload August 18, 2008 ; Last Revised August 18, 2008
by Yoshio Mimura, Kobe, Japan

8947

89472 = 80048809, and 82 + 02 + 02 + 42 + 82 + 82 + 02 + 92 = 172.

Page of Squares : First Upload August 18, 2008 ; Last Revised August 18, 2008
by Yoshio Mimura, Kobe, Japan

8950

89504 = 6416410506250000, and
62 + 42 + 12 + 62 + 42 + 12 + 02 + 502 + 622 + 502 + 02 + 02 + 02 = 8950.

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

8951

89515 = 57458963253443569751, and
52 + 72 + 42 + 52 + 82 + 92 + 62 + 32 + 22 + 52 + 342 + 42 + 32 + 52 + 692 + 72 + 512
= 52 + 72 + 42 + 582 + 92 + 62 + 32 + 252 + 32 + 442 + 32 + 52 + 62 + 92 + 72 + 512 = 8951.

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

8953

89532 = 24 + 584 + 684 + 834 = 194 + 284 + 344 + 944.

Page of Squares : First Upload August 18, 2008 ; Last Revised August 18, 2008
by Yoshio Mimura, Kobe, Japan

8954

89542 = 2252 + 2262 + 2272 + 2282 + ... + 6312.

8954, 8955, 8956 and 8957 are four consecutive integers having square factors (the 6th case).

Page of Squares : First Upload August 18, 2008 ; Last Revised December 14, 2013
by Yoshio Mimura, Kobe, Japan

8958

89582 = 80245764, and 8 * 0 - 2 + 4 * 5 * 7 * 64 = 8958.

Page of Squares : First Upload August 18, 2008 ; Last Revised August 18, 2008
by Yoshio Mimura, Kobe, Japan

8959

89592 = S2(399) + S2(561), where S2(n) = 12 + 22 + 32 + 42 + ... + n2.

98k + 212k + 305k + 346k are squares for k = 1,2,3 (312, 5172, 89592).

Page of Squares : First Upload August 18, 2008 ; Last Revised July 15, 2011
by Yoshio Mimura, Kobe, Japan

8960

89602 = 1043 + 2243 + 4083.

Page of Squares : First Upload August 18, 2008 ; Last Revised August 18, 2008
by Yoshio Mimura, Kobe, Japan

8961

89612± 2 are primes.

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

8962

89622 = 494 + 634 + 634 + 814.

89622 = 2! + 2! + 8! + 8! + 8! + 9! + 11! + 11!.

Page of Squares : First Upload August 18, 2008 ; Last Revised August 18, 2008
by Yoshio Mimura, Kobe, Japan

8963

The square root of 8963 is 94.673...., and 94 = 62 + 72 + 32.

Page of Squares : First Upload August 18, 2008 ; Last Revised August 18, 2008
by Yoshio Mimura, Kobe, Japan

8965

89652 = 243 + 1453 + 4263.

Page of Squares : First Upload August 18, 2008 ; Last Revised August 18, 2008
by Yoshio Mimura, Kobe, Japan

8970

Komachi equation: 89702 = 12 / 22 * 3452 * 62 * 782 / 92.

Page of Squares : First Upload November 16, 2010 ; Last Revised November 16, 2010
by Yoshio Mimura, Kobe, Japan

8973

89732 = 80514729, a square with different digits.

Page of Squares : First Upload August 18, 2008 ; Last Revised August 18, 2008
by Yoshio Mimura, Kobe, Japan

8975

The square root of 8975 is 94.736...., and 94 = 72 + 32 + 62.

89755 = 58233418611318359375, and
582 + 22 + 32 + 32 + 412 + 82 + 62 + 12 + 132 + 12 + 82 + 32 + 592 + 32 + 72 + 52 = 8975.

Page of Squares : First Upload August 18, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

8976

89762 = (32 + 8)(62 + 8)(162 + 8)(202 + 8) = (42 + 8)(382 + 8)(482 + 8)
= (42 + 8)(52 + 8)(62 + 8)(482 + 8) = (62 + 8)(282 + 8)(482 + 8).

The integral triangle of sides 2057, 592425, 594464 has square area 89762.

Page of Squares : First Upload October 21, 2011 ; Last Revised January 11, 2014
by Yoshio Mimura, Kobe, Japan

8978

89782 = 80604484, a square with even digits.

89782 = 674 + 674 + 674 + 674.

Page of Squares : First Upload August 18, 2008 ; Last Revised August 18, 2008
by Yoshio Mimura, Kobe, Japan

8980

89802± 3 are primes.

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

8981

89812 = 80658361, a zigzag square.

Page of Squares : First Upload August 18, 2008 ; Last Revised August 18, 2008
by Yoshio Mimura, Kobe, Japan

8983

89835 = 58493417834227025143, and
52 + 82 + 42 + 92 + 32 + 42 + 172 + 82 + 342 + 222 + 702 + 22 + 52 + 12 + 432
= 52 + 82 + 42 + 92 + 342 + 172 + 82 + 32 + 42 + 222 + 702 + 22 + 52 + 12 + 432 = 8983.

Komachi equation: 89832 = - 93 - 83 + 73 * 63 - 53 + 4323 - 13.

Page of Squares : First Upload December 8, 2008 ; Last Revised November 16, 2010
by Yoshio Mimura, Kobe, Japan

8984

89842± 3 are primes.

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

8986

89862 = 80748196, a zigzag square.

89862 = 80748196, 8074 + 8 * 19 * 6 = 8986.

89862 = 38 + 58 + 58 + 68 + 68 + 88 + 88 + 98.

Page of Squares : First Upload August 18, 2008 ; Last Revised August 18, 2008
by Yoshio Mimura, Kobe, Japan

8987

1505k + 4042k + 4988k + 6106k are squares for k = 1,2,3 (1292, 89872, 6489992).

Page of Squares : First Upload July 15, 2011 ; Last Revised July 15, 2011
by Yoshio Mimura, Kobe, Japan

8988

89882 = 1403 + 3183 + 3583.

Page of Squares : First Upload August 18, 2008 ; Last Revised August 18, 2008
by Yoshio Mimura, Kobe, Japan

8989

89892 = 80802121, a zigzag square.

Page of Squares : First Upload August 18, 2008 ; Last Revised August 18, 2008
by Yoshio Mimura, Kobe, Japan

8991

89912 = 80838081, a zigzag square pegged by 8.

Page of Squares : First Upload August 18, 2008 ; Last Revised August 18, 2008
by Yoshio Mimura, Kobe, Japan

8992

89922 = 80856064, a zigzag square.

Page of Squares : First Upload August 18, 2008 ; Last Revised August 18, 2008
by Yoshio Mimura, Kobe, Japan

8993

The square root of 8993 is 94.83142...., and 94 = 82 + 32 + 12 + 42 + 22.

89932 = 234 + 464 + 464 + 924.

Page of Squares : First Upload August 18, 2008 ; Last Revised August 18, 2008
by Yoshio Mimura, Kobe, Japan