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4200 - 4299

4200

42002 = (32 - 1)(62 - 1)(2512 - 1) = (42 - 1)(112 - 1)(992 - 1).

42002 = 403 + 2603 = 323 + 1963 + 2163 = 953 + 1053 + 2503.

Page of Squares : First Upload August 29, 2008 ; Last Revised December 28, 2013
by Yoshio Mimura, Kobe, Japan

4204

42042 = 17673616, a zigzag square.

Page of Squares : First Upload August 27, 2007 ; Last Revised August 27, 2007
by Yoshio Mimura, Kobe, Japan

4205

42052 = (73 + 74 + 75 + ... + 101)2 + (102 + 103 + 104 + ... + 130)2.

Page of Squares : First Upload August 27, 2007 ; Last Revised August 27, 2007
by Yoshio Mimura, Kobe, Japan

4206

42062 = 163 + 1313 + 2493.

42062 = 17690436, a zigzag square.

Page of Squares : First Upload August 27, 2007 ; Last Revised August 29, 2008
by Yoshio Mimura, Kobe, Japan

4207

42072 = 773 + 1773 + 2273.

Page of Squares : First Upload August 29, 2008 ; Last Revised August 29, 2008
by Yoshio Mimura, Kobe, Japan

4212

42122 = 63 + 2063 + 2083 = 1323 + 1383 + 2343.

Page of Squares : First Upload August 29, 2008 ; Last Revised August 29, 2008
by Yoshio Mimura, Kobe, Japan

4213

42132 = 883 + 1133 + 2503.

Page of Squares : First Upload August 29, 2008 ; Last Revised August 29, 2008
by Yoshio Mimura, Kobe, Japan

4214

42142 = 17757796, a square with odd digits except the last digit 6.

Komachi equations:
42142 = 982 * 72 * 62 * 52 * 432 / 2102 = 982 / 72 / 62 / 52 * 432 * 2102.

Page of Squares : First Upload October 13, 2010 ; Last Revised August 24, 2013
by Yoshio Mimura, Kobe, Japan

4216

42164 = 315938395918336, and 312 + 52 + 92 + 32 + 82 + 392 + 52 + 92 + 182 + 332 + 62 = 4216.

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

4217

42174 = 316238254381921, and 32 + 162 + 232 + 82 + 22 + 542 + 32 + 82 + 192 + 22 + 12 = 4217.

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

4223

42232 = 344 + 374 + 524 + 524.

Page of Squares : First Upload August 29, 2008 ; Last Revised August 29, 2008
by Yoshio Mimura, Kobe, Japan

4224

42242 = (32 - 1)(232 - 1)(652 - 1).

42242 = 723 + 1843 + 2243 = 853 + 1073 + 2523 = 1133 + 1963 + 2073.

A cubic polynomial :
(X + 322)(X + 22052)(X + 42242) = X3 + 47652X2 + 93151682X + 2980454402.

42242 = 17842176, 1 / 7 * 84 * 2 * 176 = 4224.

42242 = 2563 + 165 + 47.

Page of Squares : First Upload August 27, 2007 ; Last Revised December 28, 2013
by Yoshio Mimura, Kobe, Japan

4225

The square of 65.

42252 = 653 + 2603.

4225 = 652, the sum of consecutive prime 3 + 5 + 7 + 11 + ... + 199.

4225 = 652, 4 = 22 qnd 225 = 152.

Komachi equations:
42252 = 124 * 34 / 44 + 54 / 64 * 784 - 94 = 124 * 34 / 44 * 54 / 64 * 784 / 94
 = - 124 * 34 / 44 + 54 / 64 * 784 + 94.

42252 = (593 + 594 + 595 + 596 + 597)2 + (598 + 599 + 600 + 601 + 602)2.

42254 = 318644812890625, and 32 + 12 + 82 + 62 + 42 + 42 + 82 + 12 + 22 + 82 + 92 + 02 + 622 + 52 = 4225.

Page of Squares : First Upload August 27, 2007 ; Last Revised October 13, 2010
by Yoshio Mimura, Kobe, Japan

4227

42272 = 17867529, 1 + 7 * 86 * 7 + 5 - 2 + 9 = 1 * 7 * 86 * 7 - 5 + 2 * 9 = 4227.

Page of Squares : First Upload August 27, 2007 ; Last Revised August 27, 2007
by Yoshio Mimura, Kobe, Japan

4229

42292 = 813 + 1203 + 2503.

Page of Squares : First Upload August 29, 2008 ; Last Revised August 29, 2008
by Yoshio Mimura, Kobe, Japan

4231

42312 = 813 + 843 + 2563.

Page of Squares : First Upload August 29, 2008 ; Last Revised August 29, 2008
by Yoshio Mimura, Kobe, Japan

4232

42322 = 464 + 464 + 464 + 464.

Page of Squares : First Upload August 29, 2008 ; Last Revised August 29, 2008
by Yoshio Mimura, Kobe, Japan

4233

4233k + 13944k + 16434k + 27390k are squares for k = 1,2,3 (2492, 351092, 52700852).

(42332 + 3) = (12 + 3)(22 + 3)(42 + 3)(102 + 3)(182 + 3).

Page of Squares : First Upload August 27, 2007 ; Last Revised June 10, 2011
by Yoshio Mimura, Kobe, Japan

4234

42342 = (72 + 9)(82 + 9)(652 + 9).

4234 = (12 + 22 + 32 + ... + 722) / (12 + 22 + 32 + 42).

Page of Squares : First Upload November 25, 2008 ; Last Revised December 28, 2013
by Yoshio Mimura, Kobe, Japan

4236

42362 = 493 + 633 + 2603.

Page of Squares : First Upload August 29, 2008 ; Last Revised August 29, 2008
by Yoshio Mimura, Kobe, Japan

4237

42375 = 1365501935335924957 : 12 + 362 + 52 + 502 + 12 + 92 + 32 + 52 + 32 + 32 + 52 + 92 + 22 + 42 + 92 + 52 + 72 = 4237.

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

4238

42382± 3 are primes.

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

4240

42402 = (22 + 4)(42 + 4)(72 + 4)(462 + 4).

A cubic polynomial :
(X + 28202)(X + 42402)(X + 97472) = X3 + 109972X2 + 510531002X + 1165429296002.

Page of Squares : First Upload August 27, 2007 ; Last Revised December 28, 2013
by Yoshio Mimura, Kobe, Japan

4242

42422 = 17994564, 1 - 79 + 9 * 4 * 5 * 6 * 4 = 4242.

42422 = 774 x 775 + 776 x 777 + 778 x 779 + 780 x 781 + ... + 828 x 829.

Page of Squares : First Upload August 27, 2007 ; Last Revised August 27, 2007
by Yoshio Mimura, Kobe, Japan

4245

42452 = 443 + 1053 + 2563.

Page of Squares : First Upload August 29, 2008 ; Last Revised August 29, 2008
by Yoshio Mimura, Kobe, Japan

4248

42482 = 1283 + 1603 + 2283 = 1563 + 1833 + 2013.

Page of Squares : First Upload August 29, 2008 ; Last Revised August 29, 2008
by Yoshio Mimura, Kobe, Japan

4249

42492 = 1063 + 1883 + 2173.

The square root of 4249 is 65.18..., and 65 = 12 + 82.

The quadratic polynomial 4249X2 - 27104X + 52096 takes the values 1712, 1222, 952, 1082, 1512, 2062 at X = 1, 2,..., 6,

Page of Squares : First Upload August 27, 2007 ; Last Revised December 15, 2008
by Yoshio Mimura, Kobe, Japan

4250

42502± 3 are primes.

42502 = 8562 + 8572 + 8582 + 8592 + 8602 + ... + 8792.

42502 = (12 + 9)(292 + 9)(462 + 9) = (12 + 9)(42 + 9)(52 + 9)(462 + 9).

Loop of length 14 by the function f(N) = ... + c2 + b2 + a2 where N = ... + 1002c + 100b + a:
4250 - 4264 - 5860 - 6964 - ... - 1946 - 2477 - 6505 - 4250
(Note f(4250) = 422 + 502 = 4264,   f(4264) = 422 + 642 = 5860, etc. See 1946)

Page of Squares : First Upload August 27, 2007 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

4252

42522 = 743 + 1863 + 2243.

Page of Squares : First Upload August 29, 2008 ; Last Revised August 29, 2008
by Yoshio Mimura, Kobe, Japan

4256

42562 = 703 + 2023 + 2123 = 963 + 1683 + 2323.

Komachi equation: 42562 = 12 / 22 * 32 * 4562 * 72 * 82 / 92.

Page of Squares : First Upload August 29, 2008 ; Last Revised October 13, 2010
by Yoshio Mimura, Kobe, Japan

4257

42572 = 1703 + 1723 + 2013.

42572 = (11 + 12 + 13 + 14 + 15 + 16)2 + (17 + 18 + 19 + 20 + 21 + 22)2 + (23 + 24 + 25 + 26 + 27 + 28)2 + ... + (203 + 204 + 205 + 206 + 207 + 208)2.

42572 = (12 + 8)(52 + 8)(2472 + 8) = (172 + 8)(2472 + 8).

Page of Squares : First Upload August 27, 2007 ; Last Revised December 28, 2013
by Yoshio Mimura, Kobe, Japan

4261

42615 = 1404616193535657301 : 12 + 402 + 42 + 62 + 162 + 12 + 92 + 32 + 52 + 352 + 62 + 52 + 72 + 302 + 12 = 12 + 42 + 02 + 42 + 62 + 162 + 12 + 92 + 32 + 532 + 52 + 62 + 52 + 72 + 302 + 12 = 12 + 402 + 42 + 62 + 162 + 12 + 92 + 352 + 32 + 52 + 62 + 52 + 72 + 302 + 12 = 4261.

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

4263

42632± 2 are primes.

42632 = 623 + 1053 + 2563.

Page of Squares : First Upload August 29, 2008 ; Last Revised December 29, 2013
by Yoshio Mimura, Kobe, Japan

4264

42642 = (102 + 4)(182 + 4)(232 + 4) = (22 + 4)(32 + 4)(182 + 4)(232 + 4).

130k + 1937k + 4264k + 7358k are squares for k = 1,2,3 (1172, 87232, 6950972).

The sum of the squares of divisors of 4264 is a square, 49302.

Loop of length 14 by the function f(N) = ... + c2 + b2 + a2 where N = ... + 1002c + 100b + a:
4264 - 5860 - 6964 - 8857 - ... - 2477 - 6505 - 4250 - 4264
(Note f(4264) = 422 + 642 = 5860,   f(5860) = 582 + 602 = 6964, etc. See 1946)

Page of Squares : First Upload October 9, 2008 ; Last Revised December 28, 2013
by Yoshio Mimura, Kobe, Japan

4267

42672 = S2(228) + S22(349), where S2(n) 12 + 22 + 32 + 42 + ... n2.

Page of Squares : First Upload August 27, 2007 ; Last Revised August 27, 2007
by Yoshio Mimura, Kobe, Japan

4269

42692 = 253 + 1953 + 2213 = 313 + 1773 + 2333.

Page of Squares : First Upload August 29, 2008 ; Last Revised August 29, 2008
by Yoshio Mimura, Kobe, Japan

4272

Komachi equation: 42722 = 12 / 22 * 32 * 42 * 562 / 72 * 892.

Page of Squares : First Upload October 13, 2010 ; Last Revised October 13, 2010
by Yoshio Mimura, Kobe, Japan

4273

42732 = 18258529, 1 * 8 / 2 + 5 * 852 + 9 = 18 * 2 + 5 + 8 * 529 = 4273.

Page of Squares : First Upload August 27, 2007 ; Last Revised August 27, 2007
by Yoshio Mimura, Kobe, Japan

4275

42752 = 18275625, a zigzag square.

Page of Squares : First Upload August 27, 2007 ; Last Revised August 27, 2007
by Yoshio Mimura, Kobe, Japan

4277

42772 = 18292729, a zigzag square.

42772 = 18292729, 1829 + 272 * 9 = 4277.

141k + 1645k + 2773k + 4277k are squares for k = 1,2,3 (942, 53582, 3225142).

Komachi equation: 42772 = 9872 * 652 * 42 / 32 / 22 / 102.

S2(4277) = S2(6) x S2(29) x S22(46), where S2(n) 12 + 22 + 32 + 42 + ... n2.

42772 = (12 + 22 + 32 + 42 + 52 + 62)(72 + 82 + 92 + ... + 842).

Page of Squares : First Upload August 27, 2007 ; Last Revised February 2, 2013
by Yoshio Mimura, Kobe, Japan

4278

42782 = 8812 + 8822 + 8832 + 8842 + 8852 + ... + 9032.

42782 + 42792 + 42802 + ... + 43242 = 43252 + 43262 + 43272 + ... + 43702.

2790k + 4278k + 20274k + 34162k are squares for k = 1,2,3 (2482, 400522, 69499522).

42785 = 1432860469096150368 : 12 + 42 + 32 + 22 + 82 + 602 + 42 + 62 + 92 + 02 + 92 + 62 + 152 + 02 + 32 + 62 + 82 = 4278.

Page of Squares : First Upload August 27, 2007 ; Last Revised September 16, 2011
by Yoshio Mimura, Kobe, Japan

4281

42814 = 335877499495521, and 332 + 52 + 82 + 72 + 72 + 42 + 92 + 92 + 42 + 92 + 52 + 522 + 12 = 4281.

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

4284

42842 = 18352656, a zigzag square.

Cubic polynomials:
(X + 3682)(X + 5672)(X + 42842) = X3 + 43372X2 + 29032922X + 8938823042, and
(X + 5602)(X + 18632)(X + 42842) = X3 + 47052X2 + 83989082X + 44694115202.

Komachi equation: 42842 = 982 * 7652 * 42 * 32 / 2102.

Page of Squares : First Upload August 27, 2007 ; Last Revised October 13, 2010
by Yoshio Mimura, Kobe, Japan

4285

42852 = 18361225, 12 + 82 + 32 + 62 + 12 + 22 + 22 + 52 = 122.

Page of Squares : First Upload August 27, 2007 ; Last Revised August 27, 2007
by Yoshio Mimura, Kobe, Japan

4287

42872 = 74 + 144 + 544 + 564.

The square root of 4287 is 65.47..., and 65 = 42 + 72.

Page of Squares : First Upload August 27, 2007 ; Last Revised August 29, 2008
by Yoshio Mimura, Kobe, Japan

4288

42882 = (12 + 7)(32 + 7)(3792 + 7) = (112 + 7)(3792 + 7).

Page of Squares : First Upload December 28, 2013 ; Last Revised December 28, 2013
by Yoshio Mimura, Kobe, Japan

4293

42932 = 823 + 893 + 2583.

42932 = 18429849, 1 * 8 + 4298 - 4 - 9 = 4293.

Page of Squares : First Upload August 27, 2007 ; Last Revised August 29, 2008
by Yoshio Mimura, Kobe, Japan

4294

4294 = (12 + 22 + 32 + ... + 562) / (12 + 22 + 32).

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

4296

42962 = 103 + 383 + 2643.

Page of Squares : First Upload August 29, 2008 ; Last Revised August 29, 2008
by Yoshio Mimura, Kobe, Japan

4298

42982 = 34 + 394 + 394 + 614.

42982 = 18472804, a zigzag square.

Page of Squares : First Upload August 27, 2007 ; Last Revised August 29, 2008
by Yoshio Mimura, Kobe, Japan

4299

42992 = 43 + 1803 + 2333 = 633 + 953 + 2593.

42992 = 18481401, a zigzag square.

Page of Squares : First Upload August 27, 2007 ; Last Revised August 29, 2008
by Yoshio Mimura, Kobe, Japan