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8200 - 8299

8200

82002 = 104 + 304 + 304 + 904.

Loop of length 35 by the function f(N) = ... + c2 + b2 + a2 where N = ... + 1002c + 100b + a:
8200 - 6724 - 5065 - 6725 - ... - 4930 - 3301 - 1090 - 8200
(Note f(8200) = 822 + 002 = 6724,   f(6724) = 672 + 242 = 5065, etc. See 37)

Page of Squares : First Upload June 30, 2008 ; Last Revised October 9, 2008
by Yoshio Mimura, Kobe, Japan

8202

82022 = 67272804, a zigzag square.

82024 = 4525630158022416,
and 42 + 52 + 22 + 562 + 302 + 12 + 582 + 02 + 222 + 42 + 162 = 8202.

Page of Squares : First Upload June 30, 2008 ; Last Revised December 1, 2008
by Yoshio Mimura, Kobe, Japan

8203

The square root of 8203 is 90.5704...., and 90 = 52 + 72 + 02 + 42.

Page of Squares : First Upload June 30, 2008 ; Last Revised June 30, 2008
by Yoshio Mimura, Kobe, Japan

8205

The square root of 8205 is 90.581...., and 90 = 52 + 82 + 12.

82054 = 4532255050100625,
and 452 + 32 + 222 + 52 + 502 + 502 + 12 + 02 + 02 + 62 + 252 = 8205.

Page of Squares : First Upload June 30, 2008 ; Last Revised December 1, 2008
by Yoshio Mimura, Kobe, Japan

8206

517k + 869k + 3245k + 7469k are squares for k = 1,2,3 (1102, 82062, 6720342).

Page of Squares : First Upload July 12, 2011 ; Last Revised July 12, 2011
by Yoshio Mimura, Kobe, Japan

8207

82072 = 67354849, a zigzag square.

82072 = 2253 + 2803 + 3243.

Page of Squares : First Upload June 30, 2008 ; Last Revised June 30, 2008
by Yoshio Mimura, Kobe, Japan

8208

82082 = (12 + 8)(22 + 8)(122 + 8)(642 + 8) = (12 + 8)(22 + 8)(72 + 8)(82 + 8)(122 + 8)
= (12 + 8)(82 + 8)(122 + 8)(262 + 8) = (102 + 8)(122 + 8)(642 + 8)
= (22 + 8)(42 + 8)(72 + 8)(642 + 8) = (42 + 8)(262 + 8)(642 + 8)
= (42 + 8)(72 + 8)(82 + 8)(262 + 8) = (72 + 8)(82 + 8)(102 + 8)(122 + 8).

82082 = 2123 + 2383 + 3543.

Page of Squares : First Upload June 30, 2008 ; Last Revised January 11, 2014
by Yoshio Mimura, Kobe, Japan

8209

82093 = 553185473329, and 52 + 52 + 32 + 12 + 852 + 42 + 72 + 32 + 32 + 292 = 8209.

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

8211

82112 = 1143 + 2803 + 3533 = 1403 + 3133 + 3243.

82115 = 37323319338844842051 :
372 + 322 + 32 + 312 + 92 + 32 + 32 + 82 + 82 + 442 + 82 + 42 + 22 + 02 + 512 = 8211.

Page of Squares : First Upload June 30, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

8214

82142 = 373 + 4073.

Page of Squares : First Upload June 30, 2008 ; Last Revised June 30, 2008
by Yoshio Mimura, Kobe, Japan

8217

82172 = (12 + 2)(32 + 2)(92 + 2)(1572 + 2).

82172 = 344 + 614 + 664 + 764.

82172 = S2(389) + S2(523), where S2(n) = 12 + 22 + 32 + 42 + ... + n2.

Page of Squares : First Upload June 30, 2008 ; Last Revised January 11, 2014
by Yoshio Mimura, Kobe, Japan

8220

82202 = 2443 + 2903 + 3063.

Page of Squares : First Upload June 30, 2008 ; Last Revised June 30, 2008
by Yoshio Mimura, Kobe, Japan

8222

82225 = 37573994046444849632 :
372 + 52 + 732 + 92 + 92 + 42 + 02 + 42 + 62 + 42 + 42 + 42 + 82 + 42 + 92 + 62 + 322 = 8222.

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

8225

82252 = 67650625, and 676 = 262, 50625 = 2252.

Page of Squares : First Upload June 30, 2008 ; Last Revised June 30, 2008
by Yoshio Mimura, Kobe, Japan

8226

82262 = 67667076, a square with 3 kinds of digits.

Page of Squares : First Upload June 30, 2008 ; Last Revised June 30, 2008
by Yoshio Mimura, Kobe, Japan

8227

82272 = 67683529, a zigzag square.

Page of Squares : First Upload June 30, 2008 ; Last Revised June 30, 2008
by Yoshio Mimura, Kobe, Japan

8228

82282 = 224 + 444 + 444 + 884.

Page of Squares : First Upload June 30, 2008 ; Last Revised June 30, 2008
by Yoshio Mimura, Kobe, Japan

8229

82295 = 37734214305062632149 :
372 + 72 + 32 + 42 + 22 + 12 + 42 + 32 + 02 + 52 + 02 + 622 + 62 + 32 + 212 + 492
= 372 + 72 + 32 + 42 + 212 + 42 + 32 + 02 + 52 + 02 + 622 + 62 + 32 + 22 + 12 + 492 = 8229.

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

8230

Komachi equations: 82302 = 98762 * 52 / 42 / 32 * 22 */ 12.

Page of Squares : First Upload November 9, 2010 ; Last Revised November 9, 2010
by Yoshio Mimura, Kobe, Japan

8232

82322 = (12 + 3)(22 + 3)(32 + 3)(122 + 3)(372 + 3) = (12 + 3)(92 + 3)(122 + 3)(372 + 3)
= (32 + 3)(52 + 3)(122 + 3)(372 + 3).

82322 = 1963 + 3923.

Page of Squares : First Upload June 30, 2008 ; Last Revised January 11, 2014
by Yoshio Mimura, Kobe, Japan

8234

82342 = 103 + 1113 + 4053.

Page of Squares : First Upload June 30, 2008 ; Last Revised June 30, 2008
by Yoshio Mimura, Kobe, Japan

8241

82428241 = 90792.

82415 = (192 + 8)(4292 + 8).

82415 = 38010148882532457201 :
382 + 02 + 102 + 12 + 482 + 82 + 82 + 22 + 52 + 32 + 242 + 572 + 202 + 12 = 8241.

Page of Squares : First Upload June 30, 2008 ; Last Revised January 11, 2014
by Yoshio Mimura, Kobe, Japan

8246

82462 = (42 + 3)(232 + 3)(822 + 3).

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

8247

82472 = 1113 + 3053 + 3373.

Page of Squares : First Upload June 30, 2008 ; Last Revised June 30, 2008
by Yoshio Mimura, Kobe, Japan

8249

82492 = 155 + 195 + 265 + 305 + 315.

Page of Squares : First Upload June 30, 2008 ; Last Revised June 30, 2008
by Yoshio Mimura, Kobe, Japan

8250

82502 = (122 + 6)(182 + 6)(372 + 6) = (22 + 6)(122 + 6)(2132 + 6)
= (22 + 6)(32 + 6)(182 + 6)(372 + 6) = (32 + 6)(42 + 6)(122 + 6)(372 + 6).

82502 = 373 + 843 + 4073.

82502= 106 x 107 + 107 x 108 + 108 x 109 + ... + 589 x 590.

Page of Squares : First Upload June 30, 2008 ; Last Revised January 11, 2014
by Yoshio Mimura, Kobe, Japan

8254

The square root of 8254 is 90.851...., and 90 = 82 + 52 + 12.

82542 = 68128516, and 6 - 8 + 1 * 2 * 8 * 516 = 6 - 8 * 1 + 2 * 8 * 516.

82542 = 1133 + 1393 + 4003.

Page of Squares : First Upload June 30, 2008 ; Last Revised June 30, 2008
by Yoshio Mimura, Kobe, Japan

8256

82562 = 68161536, a zigzag square.

82562 + 82572 + 82582 + ... + 83202 = 83212 + 83222 + 83232 + ... + 83842.

Page of Squares : First Upload June 30, 2008 ; Last Revised September 20, 2011
by Yoshio Mimura, Kobe, Japan

8261

82612 = 68244121, and 6 + 8244 + 12 - 1 = 8261.

Page of Squares : First Upload June 30, 2008 ; Last Revised June 30, 2008
by Yoshio Mimura, Kobe, Japan

8262

82622 = 68260644, a square with even digits.

82622± 5 are primes.

82622 = (52 + 2)(72 + 2)(102 + 2)(222 + 2).

Komachi equations: 82622 = 92 * 82 * 7652 / 42 * 32 * 22 / 102.

Page of Squares : First Upload June 30, 2008 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

8263

82632 = 314 + 344 + 584 + 864.

Page of Squares : First Upload June 30, 2008 ; Last Revised June 30, 2008
by Yoshio Mimura, Kobe, Japan

8269

The square root of 8269 is 90.93...., and 90 = 92 + 32.

82695 = 38660276842847592349 :
382 + 62 + 62 + 02 + 22 + 72 + 62 + 82 + 42 + 282 + 472 + 592 + 22 + 32 + 42 + 92 = 8269.

Page of Squares : First Upload June 30, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

8270

The square root of 8270 is 90.93...., and 90 = 92 + 32.

Page of Squares : First Upload June 30, 2008 ; Last Revised June 30, 2008
by Yoshio Mimura, Kobe, Japan

8275

82752 = 68475625, a zigzag square.

Page of Squares : First Upload June 30, 2008 ; Last Revised June 30, 2008
by Yoshio Mimura, Kobe, Japan

8276

82762 = 1013 + 1803 + 3953.

Page of Squares : First Upload June 30, 2008 ; Last Revised June 30, 2008
by Yoshio Mimura, Kobe, Japan

8280

82802 = 423 + 1163 + 4063.

Page of Squares : First Upload June 30, 2008 ; Last Revised June 30, 2008
by Yoshio Mimura, Kobe, Japan

8281

8281 = (8 + 2 + 81)2 = (82 + 8 + 1)2.

82812 = 2733 + 3643.

The square of 91.

1 / 8281 = 0.000120758362516, 12 + 202 + 72 + 52 + 832 + 62 + 252 + 162 = 8281.

82812 = (830 + 831 + 832 + 833 + 834 + 835 + 836)2 + (837 + 838 + 839 + 840 + 841 + 842 + 843)2.

Page of Squares : First Upload June 30, 2008 ; Last Revised November 25, 2008
by Yoshio Mimura, Kobe, Japan

8282

82822 = (92 + 1)(102 + 1)(912 + 1).

82822 = 68591524, a zigzag square.

Page of Squares : First Upload June 30, 2008 ; Last Revised November 2, 2013
by Yoshio Mimura, Kobe, Japan

8283

82832 = 1532 + 1552 + 1572 + 1592 + 1612 + 1632 + ... + 7452.

Page of Squares : First Upload June 30, 2008 ; Last Revised June 30, 2008
by Yoshio Mimura, Kobe, Japan

8286

82862± 5 are primes.

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

8289

82894 = 4720723441965441,
and 472 + 202 + 722 + 32 + 42 + 42 + 192 + 62 + 52 + 42 + 42 + 12 = 8289.

82895 = 39130076610451540449 :
32 + 92 + 12 + 32 + 02 + 02 + 72 + 662 + 102 + 42 + 52 + 12 + 52 + 402 + 442 + 92
= 392 + 12 + 302 + 02 + 72 + 62 + 62 + 102 + 42 + 512 + 542 + 02 + 42 + 42 + 92 = 8289.

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

8291

82915 = 39177306631034122451 :
392 + 12 + 72 + 72 + 32 + 02 + 662 + 32 + 12 + 02 + 32 + 412 + 22 + 242 + 52 + 12
= 392 + 172 + 72 + 302 + 662 + 312 + 02 + 32 + 42 + 122 + 22 + 42 + 52 + 12 = 8291.

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

8293

82932 = 68773849, and 68 - 7 + 7 * 3 * 8 * 49 = 8293.

82935 = 39224582245936924693 :
32 + 92 + 222 + 42 + 52 + 822 + 22 + 42 + 52 + 92 + 32 + 62 + 92 + 242 + 62 + 92 + 32
= 32 + 92 + 222 + 42 + 52 + 822 + 242 + 52 + 92 + 32 + 62 + 92 + 22 + 42 + 62 + 92 + 32 = 8293.

Page of Squares : First Upload June 30, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

8294

82942 = 68790436, a zigzag square.

The square root of 8294 is 91.0714005...., and 91 = 02 + 72 + 12 + 42 + 02 + 02 + 52.

Page of Squares : First Upload June 30, 2008 ; Last Revised June 30, 2008
by Yoshio Mimura, Kobe, Japan

8296

82962 = 68823616, and 68 * 8 / 2 * 3 * 61 / 6 = 8296.

Page of Squares : First Upload June 30, 2008 ; Last Revised June 30, 2008
by Yoshio Mimura, Kobe, Japan

8297

82972 = 44 + 44 + 684 + 834.

Page of Squares : First Upload June 30, 2008 ; Last Revised June 30, 2008
by Yoshio Mimura, Kobe, Japan