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7100 - 7199

7100

71002 = 63 + 553 + 3693 = 943 + 2783 + 3043.

Page of Squares : First Upload April 7, 2008 ; Last Revised April 7, 2008
by Yoshio Mimura, Kobe, Japan

7102

71022 = 603 + 1473 + 3613.

Page of Squares : First Upload April 7, 2008 ; Last Revised April 7, 2008
by Yoshio Mimura, Kobe, Japan

7106

71062 = 50495236, and 52 + 02 + 42 + 92 + 52 + 22 + 32 + 62 = 142.

7106k + 33022k + 40546k + 94050k are squares for k = 1,2,3 (4182, 1078442, 305767002).
638k + 4378k + 7106k + 11594k are squares for k = 1,2,3 (1542, 143002, 14147322).

Page of Squares : First Upload April 7, 2008 ; Last Revised July 5, 2011
by Yoshio Mimura, Kobe, Japan

7108

71082 = 324 + 584 + 644 + 684.

Page of Squares : First Upload April 7, 2008 ; Last Revised April 7, 2008
by Yoshio Mimura, Kobe, Japan

7109

71095 = 18156936350131874549 :
182 + 12 + 52 + 62 + 92 + 32 + 62 + 32 + 502 + 12 + 312 + 82 + 72 + 42 + 542 + 92 = 7109.

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

7111

71115 = 18182491499287016551 :
12 + 812 + 82 + 22 + 42 + 92 + 12 + 42 + 92 + 92 + 22 + 82 + 72 + 02 + 12 + 62 + 52 + 52 + 12 = 7111.

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

7112

71122 = (12 + 7)(72 + 7)(3362 + 7) = (212 + 7)(3362 + 7).

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

7113

71135 = 18208075414611986793 :
12 + 82 + 22 + 02 + 802 + 72 + 52 + 42 + 142 + 62 + 12 + 12 + 92 + 82 + 62 + 72 + 92 + 32 = 7113.

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

7114

(71142 + 4) = (12 + 4)(32 + 4)(62 + 4)(92 + 4)(152 + 4).

Page of Squares : First Upload April 7, 2008 ; Last Revised April 7, 2008
by Yoshio Mimura, Kobe, Japan

7115

71152 = 503 + 2463 + 3293.

Page of Squares : First Upload April 7, 2008 ; Last Revised April 7, 2008
by Yoshio Mimura, Kobe, Japan

7116

71162 = 50637456, and 52 + 02 + 62 + 32 + 72 + 42 + 52 + 62 = 142.

71162 = 43 + 1983 + 3503 = 493 + 1623 + 3593.

Page of Squares : First Upload April 7, 2008 ; Last Revised April 7, 2008
by Yoshio Mimura, Kobe, Japan

7118

71185 = 18272161214279737568 :
182 + 272 + 22 + 12 + 62 + 12 + 212 + 42 + 272 + 92 + 72 + 32 + 72 + 52 + 682
= 182 + 272 + 212 + 62 + 12 + 22 + 12 + 42 + 272 + 92 + 72 + 32 + 72 + 52 + 682 = 7118.

Komachi equations: 71182 = 3583 + 35 + 97.

Page of Squares : First Upload December 8, 2008 ; Last Revised November 5, 2010
by Yoshio Mimura, Kobe, Japan

7121

71213 = 361096232561, and 32 + 62 + 12 + 02 + 92 + 622 + 32 + 22 + 562 + 12 = 7121.

Komachi equation: 71202 = 94 * 84 + 764 - 544 - 324 + 104.

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

7122

71225 = 18323559666218041632 :
12 + 82 + 322 + 32 + 552 + 92 + 62 + 62 + 62 + 22 + 12 + 82 + 02 + 412 + 62 + 322 = 7122.

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

7124

Loop of length 5 by the function f(N) = ... + c2 + b2 + a2 where N = ... + 1002c + 100b + a:
7124 - 5617 - 3425 - 1781 - ... - 3425 - 1781 - 6850 - 7124
(Note f(7124) = 712 + 242 = 5617,   f(5617) = 562 + 172 = 3425, etc. See 1781)

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

7127

71272 = 723 + 1503 + 3613 = 1573 + 2473 + 3173.

Page of Squares : First Upload April 7, 2008 ; Last Revised April 7, 2008
by Yoshio Mimura, Kobe, Japan

7128

71282 = 50808384, a zigzag square.

71282 = 4! + 5! + 7! + 10! + 10! + 10! + 11!

71282 = (12 + 8)(42 + 8)(172 + 8)(282 + 8) = (12 + 8)(82 + 8)(162 + 8)(172 + 8)
= (12 + 8)(82 + 8)(2802 + 8) = (52 + 8)(282 + 8)(442 + 8).

71282 = 903 + 2163 + 3423.

Page of Squares : First Upload April 7, 2008 ; Last Revised January 11, 2014
by Yoshio Mimura, Kobe, Japan

7130

71305 = 18426703563479300000 :
12 + 82 + 42 + 22 + 672 + 02 + 352 + 62 + 342 + 72 + 92 + 32 + 02 + 02 + 02 + 02 + 02 = 7130.

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

7132

71325 = 18452561970246802432 :
182 + 42 + 52 + 22 + 52 + 62 + 12 + 92 + 702 + 22 + 42 + 62 + 82 + 02 + 242 + 322
= 182 + 42 + 52 + 22 + 52 + 62 + 12 + 92 + 702 + 242 + 62 + 82 + 02 + 22 + 42 + 322 = 7132.

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

7133

71332 = 50879689, and 52 + 02 + 82 + 72 + 92 + 62 + 82 + 92 = 202.

Page of Squares : First Upload April 7, 2008 ; Last Revised April 7, 2008
by Yoshio Mimura, Kobe, Japan

7134

2958k + 7134k + 24708k + 33321k are squares for k = 1,2,3 (2612, 421952, 72435332).

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

7136

71362± 3 are primes.

71365 = 18504365873536434176 :
12 + 82 + 52 + 02 + 42 + 32 + 62 + 52 + 82 + 732 + 52 + 32 + 62 + 42 + 342 + 172 + 62
= 12 + 82 + 502 + 42 + 362 + 52 + 82 + 72 + 32 + 52 + 362 + 42 + 32 + 412 + 72 + 62 = 7136.

Page of Squares : First Upload December 8, 2008 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

7140

71402 = (92 - 1)(162 - 1)(502 - 1).

71402 = 198 * 199 * 200 + 200 * 201 * 202 + 202 * 203 * 204 + ... + 208 * 209 * 210..

The integral triangle of sides 7208, 14295, 16913 (or 6713, 15912, 19025)(or 1433, 77600, 78183) has square area 71402.

Komachi equation: 71402 = 12 / 22 * 342 * 52 / 62 * 72 * 82 * 92.

Page of Squares : First Upload April 7, 2008 ; Last Revised January 11, 2014
by Yoshio Mimura, Kobe, Japan

7141

Loop of length 6 by the function f(N) = b2 + a2 for N = 100b + a:
7141 - 6722 - 4973 - 7730 - 6829 - 5465 - 7141   (Note f(7141) = 712 + 412 = 6722.)

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

7144

71442 = 51036736, and 512 + 02 + 32 + 672 + 32 + 62.

7144 = (12 + 22 + 32 + ... + 472) / (12 + 22).

71445 = 18608322723436724224 :
182 + 62 + 02 + 82 + 322 + 22 + 72 + 232 + 42 + 32 + 672 + 22 + 42 + 22 + 242
= 182 + 62 + 02 + 82 + 32 + 222 + 72 + 22 + 342 + 32 + 672 + 22 + 42 + 222 + 42
= 182 + 62 + 02 + 82 + 322 + 22 + 72 + 232 + 42 + 32 + 672 + 242 + 22 + 22 + 42 = 7144.

Page of Squares : First Upload November 25, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

7145

71452 = 51051025, and 52 + 12 + 02 + 52 + 12 + 02 + 22 + 52 = 92.

71452 = 753 + 2013 + 3493.

Page of Squares : First Upload April 7, 2008 ; Last Revised April 7, 2008
by Yoshio Mimura, Kobe, Japan

7152

71522 = 203 + 2083 + 3483.

Page of Squares : First Upload April 7, 2008 ; Last Revised April 7, 2008
by Yoshio Mimura, Kobe, Japan

7154

71542 = 51179716, a square with odd digits except the last digit 6.

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

7155

71552 = (260 + 261 + 262)2 + (263 + 264 + 265)2 + (266 + 267 + 268)2 + ... + (407 + 408 + 409)2.

71554 = 2620828195700625,
and 262 + 202 + 82 + 22 + 82 + 192 + 52 + 702 + 02 + 62 + 252 = 7155.

Page of Squares : First Upload April 7, 2008 ; Last Revised December 1, 2008
by Yoshio Mimura, Kobe, Japan

7161

496k + 5270k + 7161k + 11098k are squares for k = 1,2,3 (1552, 142292, 13713472).

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

7166

71662 = 51351556, a square with odd digits except the last digit 6.

71662 = 55 + 155 + 225 + 345.

Page of Squares : First Upload April 7, 2008 ; Last Revised August 24, 2013
by Yoshio Mimura, Kobe, Japan

7167

71675 = 18909803779633220607 :
182 + 92 + 02 + 92 + 82 + 02 + 372 + 72 + 92 + 62 + 32 + 322 + 202 + 602 + 72 = 7167.

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

7168

71682 = (32 + 7)(72 + 7)(112 + 7)(212 + 7).

71682 = 324 + 644 + 644 + 644.

Page of Squares : First Upload April 7, 2008 ; Last Revised January 11, 2014
by Yoshio Mimura, Kobe, Japan

7171

71712 = 51423241, a zigzag square.

Page of Squares : First Upload April 7, 2008 ; Last Revised April 7, 2008
by Yoshio Mimura, Kobe, Japan

7172

71722 = 51437584, a zigzag square.

71722 = 84 + 164 + 684 + 744.

71723 = 368910352448, and 32 + 682 + 92 + 102 + 32 + 52 + 22 + 42 + 482 = 7172.

Page of Squares : First Upload April 7, 2008 ; Last Revised December 1, 2008
by Yoshio Mimura, Kobe, Japan

7173

71732± 2 are primes.

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

7176

71762 = 233 + 1693 + 3603 = 1003 + 2723 + 3123 = 1223 + 1563 + 3583.

Page of Squares : First Upload April 7, 2008 ; Last Revised April 7, 2008
by Yoshio Mimura, Kobe, Japan

7177

71772 = 2303 + 2363 + 2973.

Page of Squares : First Upload April 7, 2008 ; Last Revised April 7, 2008
by Yoshio Mimura, Kobe, Japan

7179

71792 = 51538041, a zigzag square.

Page of Squares : First Upload April 7, 2008 ; Last Revised April 7, 2008
by Yoshio Mimura, Kobe, Japan

7180

71802 = 185 x 186 + 186 x 187 + 187 x 188 + ... + 543 x 544.

Page of Squares : First Upload April 7, 2008 ; Last Revised April 7, 2008
by Yoshio Mimura, Kobe, Japan

7181

71812 = 643 + 1023 + 3693.

Page of Squares : First Upload April 7, 2008 ; Last Revised April 7, 2008
by Yoshio Mimura, Kobe, Japan

7182

71822 = 174 + 434 + 694 + 714.

Page of Squares : First Upload April 7, 2008 ; Last Revised April 7, 2008
by Yoshio Mimura, Kobe, Japan

7184

71844 = 2663577236340736,
and 22 + 62 + 62 + 32 + 572 + 72 + 22 + 362 + 342 + 02 + 72 + 362 = 7184.

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

7186

71862 = 51638596, a zigzag square.

71862 = 254 + 454 + 454 + 814.

Loop of length 14 by the function f(N) = ... + c2 + b2 + a2 where N = ... + 1002c + 100b + a:
7186 - 12437 - 1946 - 2477 - ... - 8731 - 8530 - 8125 - 7186
(Note f(7186) = 712 + 862 = 12437,   f(12437) = 12 + 242 + 372 = 1946, etc. See 1946)

Page of Squares : First Upload April 7, 2008 ; Last Revised October 9, 2008
by Yoshio Mimura, Kobe, Japan

7187

71872 = 51652969, and 52 + 12 + 62 + 52 + 22 + 92 + 62 + 92 = 172.

Page of Squares : First Upload April 7, 2008 ; Last Revised April 7, 2008
by Yoshio Mimura, Kobe, Japan

7188

1 / 7188 = 0.000139120756, 12 + 392 + 12 + 22 + 02 + 752 + 62 = 7188,
1 / 7188 = 0.000139120756, 12 + 392 + 12 + 22 + 0752 + 62 = 7188.

71882 = 163 + 1943 + 3543.

71883 = 371384868672, and 32 + 72 + 132 + 82 + 482 + 62 + 82 + 672 + 22 = 7188.

Page of Squares : First Upload April 7, 2008 ; Last Revised December 1, 2008
by Yoshio Mimura, Kobe, Japan

7190

71902 = 993 + 2493 + 3283.

Page of Squares : First Upload April 7, 2008 ; Last Revised April 7, 2008
by Yoshio Mimura, Kobe, Japan

7191

71912 = 51710481, and 5 + 1 + 7104 + 81 = 7191.

Page of Squares : First Upload April 7, 2008 ; Last Revised April 7, 2008
by Yoshio Mimura, Kobe, Japan

7192

71922 = 1963 + 2403 + 3123.

Page of Squares : First Upload April 7, 2008 ; Last Revised April 7, 2008
by Yoshio Mimura, Kobe, Japan

7196

71962 = 51782416, and 52 + 12 + 72 + 82 + 22 + 42 + 12 + 62 = 142.

71962 = 1943 + 2073 + 3293.

Page of Squares : First Upload April 7, 2008 ; Last Revised April 7, 2008
by Yoshio Mimura, Kobe, Japan

7197

71972 = 443 + 2203 + 3453.

Page of Squares : First Upload April 7, 2008 ; Last Revised April 7, 2008
by Yoshio Mimura, Kobe, Japan

7198

7198k + 16874k + 20650k + 80594k are squares for k = 1,2,3 (3542, 851962, 231834602).

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