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4300 - 4399

4300

1010k + 1690k + 2570k + 2830k are squares for k = 1,2,3 (902, 43002, 2133002).

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

4301

43012 = 1303 + 1543 + 2333.

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

4302

43022 = 34 + 334 + 514 + 574.

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

4305

43052± 2 are primes.

3045k + 3381k + 4305k + 5145k are squares for k = 1,2,3 (1262, 81062, 5318462).

Page of Squares : First Upload June 10, 2011 ; Last Revised December 29, 2013
by Yoshio Mimura, Kobe, Japan

4307

43072 = (176 + 177)2 + (178 + 179)2 + (180 + 181)2 + (182 + 183)2 + ... + (320 + 321)2.

Page of Squares : First Upload September 3, 2007 ; Last Revised September 3, 2007
by Yoshio Mimura, Kobe, Japan

4308

43082 = 18558864, 1 * 8 + 5 * 5 * 8 * 86 / 4 = 4308.

Page of Squares : First Upload September 3, 2007 ; Last Revised September 3, 2007
by Yoshio Mimura, Kobe, Japan

4309

(43092 + 5) = (42 + 5)(82 + 5)(92 + 5)(122 + 5).

43092 = 18567481, 12 + 82 + 52 + 62 + 72 + 42 + 82 + 12 = 162.

43095 = 1485533570103220549 : 12 + 42 + 82 + 52 + 52 + 332 + 52 + 72 + 02 + 12 + 02 + 32 + 22 + 22 + 02 + 542 + 92 = 4309.

Page of Squares : First Upload September 3, 2007 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

4310

43102 = 18576100, 1 * 8 * 5 + 7 * 610 + 0 = 4310.

Page of Squares : First Upload September 3, 2007 ; Last Revised September 3, 2007
by Yoshio Mimura, Kobe, Japan

4312

43122 = 873 + 1053 + 2563.

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

4318

43182 = 18645124, 1 + 864 * 5 - 1 + 2 - 4 = 1 * 864 * 5 + 1 * 2 - 4 = 1 * 864 * 5 - 1 / 2 * 4
  = 1 * 864 * 5 * 1 + 2 - 4 = 1 + 864 * 5 - 12 / 4 = 4318.

Page of Squares : First Upload September 3, 2007 ; Last Revised September 3, 2007
by Yoshio Mimura, Kobe, Japan

4319

43194 = 347962799445121, and 342 + 72 + 92 + 62 + 272 + 92 + 92 + 442 + 52 + 122 + 12 = 4319.

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

4320

43202 = (22 - 1)(32 - 1)(52 - 1)(72 - 1)(262 - 1) = (22 - 1)(42 - 1)(52 - 1)(72 - 1)(192 - 1)
= (42 - 1)(72 - 1)(1612 - 1).

43202 = 83 + 643 + 2643 = 363 + 603 + 2643 = 783 + 1883 + 2263.

43202 = 18662400, 18 * 6 / 6 * 240 + 0 = 18 / 6 * 6 * 240 + 0 = 4320.

782 + 4320 = 1022, 782 - 4320 = 422.

Page of Squares : First Upload September 3, 2007 ; Last Revised December 28, 2013
by Yoshio Mimura, Kobe, Japan

4322

The square root of 4322 is 65.74...., and 65 = 72 + 42.

Page of Squares : First Upload September 3, 2007 ; Last Revised September 3, 2007
by Yoshio Mimura, Kobe, Japan

4326

43292 = (12 + 5)(32 + 5)(4722 + 5).

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

4327

1 / 4327 = 0.00023110700254217, 22 + 312 + 102 + 72 + 0022 + 542 + 22 + 172 = 4327.

Page of Squares : First Upload September 3, 2007 ; Last Revised September 3, 2007
by Yoshio Mimura, Kobe, Japan

4329

43292 = 364 + 454 + 604 = 55 + 95 + 195 + 235 + 255.

43292 = 18740241, 1 * 8740 / 2 - 41 = 4329.

390k + 2262k + 4329k + 6708k are squares for k = 1,2,3 (1172, 83072, 6281732).

Page of Squares : First Upload September 3, 2007 ; Last Revised June 10, 2011
by Yoshio Mimura, Kobe, Japan

4331

The square root of N is 65.81..., and 65 = 82 + 12, for N = 4331, 4332.

Page of Squares : First Upload September 3, 2007 ; Last Revised September 3, 2007
by Yoshio Mimura, Kobe, Japan

4332

43322 = 383 + 1903 + 2283 = 573 + 1523 + 2473 = 663 + 1693 + 2393.

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

4333

43332 = 18774889, 1 * 877 + 48 * 8 * 9 = 18 - 77 + 488 * 9 = 4333.

Page of Squares : First Upload September 3, 2007 ; Last Revised September 3, 2007
by Yoshio Mimura, Kobe, Japan

4337

Cubic polynomials:
(X + 3682)(X + 5672)(X + 42842) = X3 + 43372X2 + 29032922X+ 8938823042, and
(X + 19352)(X + 26882)(X + 28002) = X3 + 43372X2 + 106327202X + 145635840002.

Page of Squares : First Upload September 3, 2007 ; Last Revised September 3, 2007
by Yoshio Mimura, Kobe, Japan

4339

1 / 4339 = 0.0002304..., and 2304 = 482.

Page of Squares : First Upload September 3, 2007 ; Last Revised September 3, 2007
by Yoshio Mimura, Kobe, Japan

4341

43412 = 18844281, 1 * 8 * 8 - 4 + 4281 = 1 - 88 + 4428 * 1 = 1 * 8844 / 2 - 81 = 4341.

Page of Squares : First Upload September 3, 2007 ; Last Revised September 3, 2007
by Yoshio Mimura, Kobe, Japan

4342

43422 = 18852964, 18 + 8 * 5 * 2 * 9 * 6 + 4 = 4342.

Page of Squares : First Upload September 3, 2007 ; Last Revised September 3, 2007
by Yoshio Mimura, Kobe, Japan

4343

43432 = 18861649, and 12 + 82 + 82 + 62 + 12 + 642 + 92.

43435 = 1545073510425529943, and 12 + 52 + 452 + 02 + 72 + 352 + 12 + 02 + 42 + 22 + 52 + 52 + 292 + 92 + 42 + 32 = 4343.

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

4344

43442 = (12 + 3)(32 + 3)(6272 + 3).

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

4346

43462 = 18887716, 18 + 88 * 7 * 7 + 16 = 4346.

Page of Squares : First Upload September 3, 2007 ; Last Revised September 3, 2007
by Yoshio Mimura, Kobe, Japan

4347

43472 = (22 + 5)(42 + 5)(82 + 5)(382 + 5).

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

4350

43502 = (12 + 9)(42 + 9)(72 + 9)(362 + 9) = (22 + 6)(32 + 6)(92 + 6)(382 + 6) = (92 + 6)(122 + 6)(382 + 6).

A 4x4 perfect magic square consisting of squares, the constant being 4350.

42532 22392
542172282192
72262512322
372242312302

Komachi equation: 43502 = 92 * 872 / 62 * 52 * 42 / 32 / 22 * 102.

Page of Squares : First Upload September 3, 2007 ; Last Revised December 28, 2013
by Yoshio Mimura, Kobe, Japan

4352

43522 = 164 + 324 + 324 + 644.

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

4353

43532 = 573 + 923 + 2623.

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

4356

The square of 66.

43562± 5 are primes.

43562 = (12 + 8)(52 + 8)(62 + 8)(382 + 8) = (62 + 8)(172 + 8)(382 + 8).

43562 = 663 + 663 + 2643.

Page of Squares : First Upload September 3, 2007 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

4361

43612 = 15 + 15 + 155 + 165 + 285.

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

4362

The square root of 4362 is 66.04543...., and 66 = 02 + 42 + 52 + 42 + 32.

Komachi equation: 43622 = 982 / 72 * 65432 / 212.

Page of Squares : First Upload September 3, 2007 ; Last Revised October 13, 2010
by Yoshio Mimura, Kobe, Japan

4364

The quadratic polynomial -4364X2 + 44716X - 37751 takes the values 512, 1852, 2392, 2672, 2772, 2712 at X = 1, 2,..., 6,

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

4366

43662 = 19061956, a zigzag square.

Page of Squares : First Upload September 3, 2007 ; Last Revised September 3, 2007
by Yoshio Mimura, Kobe, Japan

4368

43682 = (12 + 3)(22 + 3)(32 + 3)(52 + 3)(62 + 3)(72 + 3)
= (12 + 3)(22 + 3)(32 + 3)(52 + 3)(452 + 3) = (12 + 3)(22 + 3)(32 + 3)(72 + 3)(332 + 3)
= (12 + 3)(32 + 3)(192 + 3)(332 + 3) = (12 + 3)(32 + 3)(52 + 3)(62 + 3)(192 + 3)
= (12 + 3)(52 + 3)(62 + 3)(72 + 3)(92 + 3) = (12 + 3)(52 + 3)(92 + 3)(452 + 3)
= (12 + 3)(72 + 3)(92 + 3)(332 + 3) = (132 - 1)(3372 - 1) = (32 + 3)(52 + 3)(72 + 3)(332 + 3)
= (32 + 3)(72 + 3)(92 + 3)(192 + 3).

A cubic polynomial :
(X + 10442)(X + 26392)(X + 43682) = X3 + 52092X2 + 126988682X + 120343466882.

Komachi equations:
43682 = 122 * 32 / 42 + 562 * 782 - 92 = 122 * 32 / 42 * 562 * 782 / 92
 = - 122 * 32 / 42 + 562 * 782 + 92.

Page of Squares : First Upload September 3, 2007 ; Last Revised December 28, 2013
by Yoshio Mimura, Kobe, Japan

4374

43742 = 813 + 1623 + 2433 = 97 + 97 + 97 + 97.

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

4375

43752 = 493 + 1273 + 2573 = 254 + 504 + 504 + 504.

43752 = 19140625, a zigzag square.

43752 = 30 + 37 + 38 + 314 + 315.

1 / 4375 = 0.00022857142857, 22 + 22 + 82 + 52 + 72 + 142 + 282 + 572 = 4375,
1 / 4375 = 0.00022857142857, 22 + 22 + 82 + 572 + 142 + 282 + 52 + 72 = 4375,
1 / 4375 = 0.00022857142857, 22 + 282 + 52 + 72 + 142 + 22 + 82 + 572 = 4375,
1 / 4375 = 0.00022857142857, 22 + 282 + 572 + 142 + 22 + 82 + 52 + 72 = 4375.

Page of Squares : First Upload September 3, 2007 ; Last Revised August 30, 2011
by Yoshio Mimura, Kobe, Japan

4378

638k + 4378k + 7106k + 11594k are squares for k = 1,2,3 (1542, 143002, 14147322).

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

4379

The square root of 4379 is 66.174...., and 66 = 12 + 72 + 42.

Page of Squares : First Upload September 3, 2007 ; Last Revised September 3, 2007
by Yoshio Mimura, Kobe, Japan

4380

The square root of 4380 is 66.181...., and 66 = 12 + 82 + 12.

762k + 1938k + 2334k + 3066k are squares for k = 1,2,3 (902, 43802, 2219402).

Page of Squares : First Upload September 3, 2007 ; Last Revised June 10, 2011
by Yoshio Mimura, Kobe, Japan

4382

43822 = 94 + 374 + 514 + 574.

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

4383

43832 = 124 + 124 + 214 + 664.

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

4384

43842 = 19219456, 1 + 9 + 219 * 4 * 5 - 6 = 4384.

Page of Squares : First Upload September 3, 2007 ; Last Revised September 3, 2007
by Yoshio Mimura, Kobe, Japan

4386

43862 = (102 + 2)(162 + 2)(272 + 2).

43862 = 443 + 493 + 2673.

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

4389

43892 = 19263321, 19 * 2 / 6 * 33 * 21 = 4389.

Page of Squares : First Upload September 3, 2007 ; Last Revised September 3, 2007
by Yoshio Mimura, Kobe, Japan

4392

43922 = 184 + 184 + 184 + 664.

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

4393

43932 = 19298449, 1 + 9 / 2 * 984 - 4 * 9 = 4393.

43932 = (42 + 7)(9162 + 7).

Page of Squares : First Upload September 3, 2007 ; Last Revised December 28, 2013
by Yoshio Mimura, Kobe, Japan

4394

43942 = 136 + 136 + 136 + 136.

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

4398

43982 = 19342404, a zigzag square.

Page of Squares : First Upload September 3, 2007 ; Last Revised September 3, 2007
by Yoshio Mimura, Kobe, Japan

4399

43992 = 19351201, a zigzag square.

Page of Squares : First Upload September 3, 2007 ; Last Revised September 3, 2007
by Yoshio Mimura, Kobe, Japan