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, 2011by Yoshio Mimura, Kobe, Japan
4301
43012 = 1303 + 1543 + 2333.
Page of Squares : First Upload August 29, 2008 ; Last Revised August 29, 2008by Yoshio Mimura, Kobe, Japan
4302
43022 = 34 + 334 + 514 + 574.
Page of Squares : First Upload August 29, 2008 ; Last Revised August 29, 2008by 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, 2013by 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, 2007by 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, 2007by 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, 2008by 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, 2007by Yoshio Mimura, Kobe, Japan
4312
43122 = 873 + 1053 + 2563.
Page of Squares : First Upload August 29, 2008 ; Last Revised August 29, 2008by 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.
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, 2008by 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, 2013by 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, 2007by Yoshio Mimura, Kobe, Japan
4326
43292 = (12 + 5)(32 + 5)(4722 + 5).
Page of Squares : First Upload December 28, 2013 ; Last Revised December 28, 2013by 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, 2007by 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, 2011by 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, 2007by 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, 2008by 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, 2007by 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.
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, 2007by 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, 2007by 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, 2007by 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, 2008by Yoshio Mimura, Kobe, Japan
4344
43442 = (12 + 3)(32 + 3)(6272 + 3).
Page of Squares : First Upload December 28, 2013 ; Last Revised December 28, 2013by 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, 2007by 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, 2013by 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.
|
Komachi equation: 43502 = 92 * 872 / 62 * 52 * 42 / 32 / 22 * 102.
Page of Squares : First Upload September 3, 2007 ; Last Revised December 28, 2013by Yoshio Mimura, Kobe, Japan
4352
43522 = 164 + 324 + 324 + 644.
Page of Squares : First Upload August 29, 2008 ; Last Revised August 29, 2008by Yoshio Mimura, Kobe, Japan
4353
43532 = 573 + 923 + 2623.
Page of Squares : First Upload August 29, 2008 ; Last Revised August 29, 2008by 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, 2014by Yoshio Mimura, Kobe, Japan
4361
43612 = 15 + 15 + 155 + 165 + 285.
Page of Squares : First Upload August 29, 2008 ; Last Revised August 29, 2008by 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, 2010by 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, 2008by Yoshio Mimura, Kobe, Japan
4366
43662 = 19061956, a zigzag square.
Page of Squares : First Upload September 3, 2007 ; Last Revised September 3, 2007by 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.
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, 2008by 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.
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, 2011by 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, 2007by 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, 2011by Yoshio Mimura, Kobe, Japan
4382
43822 = 94 + 374 + 514 + 574.
Page of Squares : First Upload August 29, 2008 ; Last Revised August 29, 2008by Yoshio Mimura, Kobe, Japan
4383
43832 = 124 + 124 + 214 + 664.
Page of Squares : First Upload August 29, 2008 ; Last Revised August 29, 2008by 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, 2007by 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, 2013by 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, 2007by Yoshio Mimura, Kobe, Japan
4392
43922 = 184 + 184 + 184 + 664.
Page of Squares : First Upload August 29, 2008 ; Last Revised August 29, 2008by 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, 2013by Yoshio Mimura, Kobe, Japan
4394
43942 = 136 + 136 + 136 + 136.
Page of Squares : First Upload August 29, 2008 ; Last Revised August 29, 2008by Yoshio Mimura, Kobe, Japan
4398
43982 = 19342404, a zigzag square.
Page of Squares : First Upload September 3, 2007 ; Last Revised September 3, 2007by Yoshio Mimura, Kobe, Japan
4399
43992 = 19351201, a zigzag square.
Page of Squares : First Upload September 3, 2007 ; Last Revised September 3, 2007by Yoshio Mimura, Kobe, Japan