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9000 - 9099

9000

90002 = 403 + 683 + 4323 = 3003 + 3003 + 3003.

Page of Squares : First Upload August 26, 2008 ; Last Revised August 26, 2008
by Yoshio Mimura, Kobe, Japan

9001

90012 = 81018001, a square with just 3 kinds of digits.

90012 = 2323 + 2783 + 3613.

Page of Squares : First Upload August 26, 2008 ; Last Revised August 26, 2008
by Yoshio Mimura, Kobe, Japan

9004

90042 = 1943 + 3063 + 3563.

17k + 91k + 299k + 377k are squares for k = 1,2,3 (282, 4902, 90042).

Page of Squares : First Upload August 26, 2008 ; Last Revised July 15, 2011
by Yoshio Mimura, Kobe, Japan

9005

90052 = 81090025, and
8 + 1 * 0 + 9002 - 5 = 8 - 1 * 0 + 9002 - 5 = 8 * 1 + 0 + 9002 - 5 = 8 + 10 * 900 + 2 - 5
= 8 - 10 + 9002 + 5 = 9005.

90055 = 59213207351278128125, and
52 + 92 + 22 + 132 + 22 + 02 + 72 + 352 + 12 + 22 + 72 + 82 + 122 + 812 + 252
= 52 + 92 + 22 + 132 + 22 + 02 + 72 + 352 + 122 + 72 + 82 + 12 + 22 + 812 + 252
= 52 + 92 + 22 + 12 + 32 + 22 + 02 + 732 + 512 + 22 + 72 + 82 + 122 + 82 + 12 + 252
= 52 + 92 + 22 + 132 + 22 + 02 + 72 + 352 + 122 + 72 + 812 + 22 + 82 + 12 + 252 = 9005.

Page of Squares : First Upload August 26, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

9008

90082 = 2563 + 2683 + 3563.

Page of Squares : First Upload August 26, 2008 ; Last Revised August 26, 2008
by Yoshio Mimura, Kobe, Japan

9009

90092 = 13 - 23 + 33 - 43 + 53 - 63 + ... - 5443 + 5453.

Page of Squares : First Upload August 26, 2008 ; Last Revised August 26, 2008
by Yoshio Mimura, Kobe, Japan

9010

90102 = 252 + 262 + 272 + 282 + 292 + ... + 6242.

90102 = (12 + 1)(22 + 1)(42 + 1)(232 + 1)(302 + 1) = (132 + 1)(232 + 1)(302 + 1)
= (32 + 1)(42 + 1)(232 + 1)(302 + 1)(12 + 4)(72 + 4)(92 + 4)(602 + 4) = (12 + 9)(162 + 9)(1752 + 9).

Page of Squares : First Upload August 26, 2008 ; Last Revised January 11, 2014
by Yoshio Mimura, Kobe, Japan

9016

90162 = 81288256, and 81 * 28 * 8 / 2 - 56 = 9016.

90164 = 6607780563521536, and
62 + 62 + 02 + 72 + 782 + 02 + 52 + 62 + 352 + 22 + 152 + 362 = 9016.

Page of Squares : First Upload August 26, 2008 ; Last Revised December 1, 2008
by Yoshio Mimura, Kobe, Japan

9018

1 / 9018 = 0.000110889...., and 110889 = 3332.

Page of Squares : First Upload August 26, 2008 ; Last Revised August 26, 2008
by Yoshio Mimura, Kobe, Japan

9023

90232 = 384 + 464 + 674 + 864.

Page of Squares : First Upload August 26, 2008 ; Last Revised August 26, 2008
by Yoshio Mimura, Kobe, Japan

9024

90242 = 81432576, a square with different digits.

Page of Squares : First Upload August 26, 2008 ; Last Revised August 26, 2008
by Yoshio Mimura, Kobe, Japan

9025

The square of 95.

90252 = 81450625, and 8 + 1 * 4506 * 2 + 5 = 8 * 1 + 4506 * 2 + 5 = 9025.

Komachi equation: 90252 = 94 / 84 * 764 / 544 * 34 * 24 * 104.

Page of Squares : First Upload August 26, 2008 ; Last Revised November 19, 2008
by Yoshio Mimura, Kobe, Japan

9028

90282 = 84 + 624 + 764 + 764.

Page of Squares : First Upload August 26, 2008 ; Last Revised August 26, 2008
by Yoshio Mimura, Kobe, Japan

9030

90302 = (92 + 5)(102 + 5)(952 + 5).

90302 = (220 + 221 + 222 + 223)2 + (224 + 225 + 226 + 227)2 + (228 + 229 + 230 + 231)2 + ... + (412 + 413 + 414 + 415)2.

The integral triangle of sides 12943, 33625, 45882 (or 2107, 78282, 78625)(or 6361, 159054, 165335) has square area 90302.

Komachi equations:
90302 = 92 * 82 * 72 / 62 * 52 * 432 / 22 */ 12 = 982 / 72 * 62 * 52 * 432 / 22 */ 12.

Page of Squares : First Upload August 26, 2008 ; Last Revised January 11, 2014
by Yoshio Mimura, Kobe, Japan

9035

90352 = 81631225, and 82 + 12 + 62 + 32 + 12 + 22 + 22 + 52 = 122.

Page of Squares : First Upload August 26, 2008 ; Last Revised August 26, 2008
by Yoshio Mimura, Kobe, Japan

9036

90362 = 503 + 2043 + 4183 = 1093 + 3233 + 3603.

90362 = 81649296, a zigzag square.

90362 = 81649296, and 816 / 4 + 92 * 96 = 9036.

90365 = 60239465707003186176, and
62 + 02 + 22 + 32 + 92 + 42 + 62 + 52 + 72 + 02 + 702 + 02 + 32 + 12 + 82 + 612 + 72 + 62
= 62 + 02 + 22 + 32 + 92 + 42 + 62 + 52 + 702 + 72 + 02 + 02 + 32 + 12 + 82 + 612 + 72 + 62 = 9036.

Page of Squares : First Upload August 26, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

9037

90372 = 2493 + 3013 + 3393.

Page of Squares : First Upload August 26, 2008 ; Last Revised August 26, 2008
by Yoshio Mimura, Kobe, Japan

9038

90385 = 60306161300230355168, and
602 + 32 + 02 + 62 + 12 + 62 + 12 + 302 + 02 + 232 + 02 + 352 + 512 + 62 + 82
= 602 + 302 + 62 + 12 + 62 + 12 + 32 + 02 + 02 + 232 + 02 + 352 + 512 + 62 + 82 = 9038.

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

9040

Komachi equation: 90402 = 12 * 22 * 32 * 42 * 52 * 6782 / 92.

Page of Squares : First Upload November 19, 2010 ; Last Revised November 19, 2010
by Yoshio Mimura, Kobe, Japan

9041

90412 = 81739681, a zigzag square.

90415 = 60406315443285101201, and
602 + 402 + 62 + 32 + 152 + 42 + 42 + 32 + 282 + 512 + 02 + 122 + 02 + 12 = 9041.

Page of Squares : First Upload August 26, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

9042

90422 = 81757764, and 82 + 12 + 72 + 52 + 72 + 72 + 62 + 42 = 172.

90425 = 60439729711437011232, and
62 + 02 + 42 + 392 + 72 + 22 + 92 + 72 + 12 + 12 + 432 + 702 + 12 + 12 + 232 + 22 = 9042.

Page of Squares : First Upload August 26, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

9043

90432 = 95 + 105 + 265 + 305 + 345.

Page of Squares : First Upload August 26, 2008 ; Last Revised August 26, 2008
by Yoshio Mimura, Kobe, Japan

9045

90455 = 60540061245962653125, and
602 + 52 + 42 + 02 + 02 + 62 + 122 + 42 + 592 + 62 + 262 + 52 + 312 + 22 + 52 = 9045.

90452 + 90462 + 90472 + ... + 91122 = 91132 + 91142 + 91152 + ... + 91792.

Komachi equations:
90452 = 12 * 22 * 32 * 42 * 52 * 672 / 82 * 92 = 12 / 22 * 32 / 42 * 52 * 672 * 82 * 92.

Page of Squares : First Upload December 8, 2008 ; Last Revised September 20, 2011
by Yoshio Mimura, Kobe, Japan

9046

90462 = 1813 + 2553 + 3903.

Page of Squares : First Upload August 26, 2008 ; Last Revised August 26, 2008
by Yoshio Mimura, Kobe, Japan

9047

90472 = 5012 + 5022 + 5032 + 5042 + 5052 + ... + 7182.

Page of Squares : First Upload August 26, 2008 ; Last Revised August 26, 2008
by Yoshio Mimura, Kobe, Japan

9048

90482 = 81866304, and 8 * 186 * 6 + 30 * 4 = 9048.

90485 = 60640525978653523968, and
62 + 02 + 62 + 402 + 52 + 22 + 52 + 92 + 72 + 82 + 652 + 32 + 522 + 32 + 92 + 62 + 82
= 62 + 02 + 62 + 402 + 522 + 52 + 92 + 72 + 82 + 652 + 32 + 52 + 22 + 32 + 92 + 62 + 82 = 9048.

Page of Squares : First Upload August 26, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

9050

90502 = 81902500 with 81 = 92 and 902500 = 9502.

Page of Squares : First Upload August 26, 2008 ; Last Revised August 26, 2008
by Yoshio Mimura, Kobe, Japan

9051

The square root of 9051 is 95.1367...., and 95 = 12 + 32 + 62 + 72.

Page of Squares : First Upload August 26, 2008 ; Last Revised August 26, 2008
by Yoshio Mimura, Kobe, Japan

9053

90532 = 893 + 3043 + 3763.

The square root of 9053 is 95.14725...., and 95 = 12 + 42 + 72 + 22 + 52.

90534 = 6716918541462481, and
672 + 162 + 92 + 12 + 82 + 52 + 42 + 142 + 622 + 42 + 82 + 12 = 9053.

Page of Squares : First Upload August 26, 2008 ; Last Revised December 1, 2008
by Yoshio Mimura, Kobe, Japan

9055

90552 = 703 + 2893 + 3863 = 983 + 1693 + 4243 = 1163 + 3223 + 3613.

90555 = 60875462426031409375, and
62 + 02 + 82 + 72 + 542 + 62 + 242 + 22 + 602 + 32 + 12 + 402 + 92 + 32 + 72 + 52
= 602 + 82 + 72 + 542 + 62 + 242 + 22 + 62 + 02 + 32 + 12 + 402 + 92 + 32 + 72 + 52 = 9055.

Page of Squares : First Upload August 26, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

9056

90562 = 82011136, and 820 * 1 * 11 + 36 = 820 * 11 + 1 * 36 = 820 * 11 * 1 + 36 = 9056.

90565 = 60909084132063051776, and
62 + 02 + 92 + 02 + 92 + 02 + 82 + 412 + 32 + 202 + 632 + 02 + 512 + 72 + 72 + 62 = 9056.

Page of Squares : First Upload August 26, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

9058

90582 = 414 + 714 + 714 + 734.

154k + 3038k + 3626k + 9058k are squares for k = 1,2,3 (1262, 102202, 9049322).

Page of Squares : First Upload August 26, 2008 ; Last Revised July 15, 2011
by Yoshio Mimura, Kobe, Japan

9060

90602 = 693 + 1313 + 4303 = 2763 + 2993 + 3253.

Page of Squares : First Upload August 26, 2008 ; Last Revised August 26, 2008
by Yoshio Mimura, Kobe, Japan

9062

90622 = 2143 + 3153 + 3453.

Page of Squares : First Upload August 26, 2008 ; Last Revised August 26, 2008
by Yoshio Mimura, Kobe, Japan

9063

90632 = 364 + 564 + 714 + 824.

90635 = 61144852257945681543, and
62 + 112 + 442 + 82 + 52 + 222 + 572 + 92 + 42 + 52 + 62 + 82 + 12 + 542 + 32
= 62 + 12 + 142 + 482 + 522 + 252 + 72 + 92 + 42 + 52 + 62 + 82 + 12 + 542 + 32
= 612 + 82 + 22 + 22 + 52 + 02 + 102 + 92 + 702 + 32 + 32 + 42 + 82 + 52 + 62 + 42 + 32 = 9083.

Page of Squares : First Upload August 26, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

9064

90642 = 113 + 1813 + 4243.

Page of Squares : First Upload August 26, 2008 ; Last Revised August 26, 2008
by Yoshio Mimura, Kobe, Japan

9065

90652 = (80 + 81 + 82 + ... + 128)2 + (129 + 130 + 131 + ... + 177)2.

Page of Squares : First Upload August 26, 2008 ; Last Revised August 26, 2008
by Yoshio Mimura, Kobe, Japan

9068

90682 = 82228624, a square with even digits.

90682 = 82228624, 82 + 22 + 22 + 22 + 82 + 62 + 22 + 42 = 142.

Page of Squares : First Upload August 26, 2008 ; Last Revised August 26, 2008
by Yoshio Mimura, Kobe, Japan

9071

1 / 9071 = 0.000110241428728, 112 + 02 + 242 + 12 + 42 + 22 + 872 + 282 = 9071,
1 / 9071 = 0.000110241428728, 112 + 0242 + 12 + 42 + 22 + 872 + 282 = 9071.

Page of Squares : First Upload August 26, 2008 ; Last Revised August 26, 2008
by Yoshio Mimura, Kobe, Japan

9072

90722 = 2103 + 2223 + 3963 = 244 + 484 + 724 + 844 = 364 + 724 + 724 + 724.

Komachi equations:
90722 = 92 * 82 * 72 * 62 * 52 * 42 * 32 / 22 / 102 = 92 * 82 * 72 * 62 / 52 / 42 * 32 * 22 * 102.

Page of Squares : First Upload August 26, 2008 ; Last Revised November 19, 2010
by Yoshio Mimura, Kobe, Japan

9073

90732 = 2163 + 2263 + 3933.

Page of Squares : First Upload August 26, 2008 ; Last Revised August 26, 2008
by Yoshio Mimura, Kobe, Japan

9075

90752 = 1653 + 2753 + 3853.

90752 = (12 + 22)(32 + 42)(52 + 62 + 72 + ... + 1252).

Page of Squares : First Upload August 26, 2008 ; Last Revised February 2, 2013
by Yoshio Mimura, Kobe, Japan

9076

1 / 9076 = 0.000110180696342, 12 + 12 + 02 + 182 + 0692 + 632 + 42 + 22 = 9076,
1 / 9076 = 0.000110180696342, 12 + 12 + 0182 + 02 + 692 + 632 + 42 + 22 = 9076,
1 / 9076 = 0.000110180696342, 12 + 12 + 0182 + 0692 + 632 + 42 + 22 = 9076.

Page of Squares : First Upload August 26, 2008 ; Last Revised August 26, 2008
by Yoshio Mimura, Kobe, Japan

9078

90782 = (12 + 2)(242 + 2)(2182 + 2).

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

9079

90792 = 82428241, a zigzag square.

90792 = 82428241.

Page of Squares : First Upload August 26, 2008 ; Last Revised August 26, 2008
by Yoshio Mimura, Kobe, Japan

9080

90802 = 363 + 2643 + 4003.

Page of Squares : First Upload August 26, 2008 ; Last Revised August 26, 2008
by Yoshio Mimura, Kobe, Japan

9084

90842± 5 are primes.

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

9086

90862 = 813 + 3143 + 3713.

Page of Squares : First Upload August 26, 2008 ; Last Revised August 26, 2008
by Yoshio Mimura, Kobe, Japan

9087

90872 = 653 + 2883 + 3883 = 215 + 235 + 255 + 255 + 355.

Page of Squares : First Upload August 26, 2008 ; Last Revised August 26, 2008
by Yoshio Mimura, Kobe, Japan

9088

90882 = 82591744, and 82 + 22 + 52 + 92 + 12 + 72 + 42 + 42 = 162.

Page of Squares : First Upload August 26, 2008 ; Last Revised August 26, 2008
by Yoshio Mimura, Kobe, Japan

9089

90892 = 82609921, 8260 + 9 * 92 + 1 = 9089.

Page of Squares : First Upload August 26, 2008 ; Last Revised August 26, 2008
by Yoshio Mimura, Kobe, Japan

9090

90902 = (32 + 9)(302 + 9)(712 + 9).

90902 = 1963 + 3173 + 3513.

Page of Squares : First Upload August 26, 2008 ; Last Revised January 11, 2014
by Yoshio Mimura, Kobe, Japan

9091

90912 = 82646281, a zigzag square.

90912 = 82646281, and 82 + 22 + 62 + 42 + 62 + 22 + 82 + 12 = 152.

Page of Squares : First Upload August 26, 2008 ; Last Revised August 26, 2008
by Yoshio Mimura, Kobe, Japan

9092

90922 = 82664464, a square with even digits.

90925 = 62129396527639135232, and
62 + 22 + 122 + 92 + 32 + 92 + 62 + 52 + 272 + 632 + 92 + 132 + 522 + 322 = 9092.

Page of Squares : First Upload August 26, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

9093

90935 = 62163571112360928693, and
62 + 22 + 12 + 62 + 352 + 72 + 12 + 112 + 22 + 32 + 62 + 02 + 92 + 22 + 862 + 92 + 32
= 62 + 22 + 12 + 62 + 352 + 72 + 112 + 12 + 22 + 32 + 62 + 02 + 92 + 22 + 862 + 92 + 32 = 9093.

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

9094

90943 = 752081402584, and 752 + 22 + 02 + 82 + 12 + 42 + 02 + 22 + 582 + 42 = 9094.

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

9096

90962 = 82737216, and 82 / 7 * 37 * 21 - 6 = 9096.

Page of Squares : First Upload August 26, 2008 ; Last Revised August 26, 2008
by Yoshio Mimura, Kobe, Japan