logo
3800 - 3899

3800

38002 = 14440000, and 144 = 122, 40000 = 2002.

Page of Squares : First Upload July 23, 2007 ; Last Revised July 23, 2007
by Yoshio Mimura, Kobe, Japan

3801

38012 = 493 + 543 + 2423.

The square root of 3801 is 61.65..., and 61 = 62 + 52.

Page of Squares : First Upload July 23, 2007 ; Last Revised August 22, 2008
by Yoshio Mimura, Kobe, Japan

3807

38072± 2 are primes.

38072 = 783 + 1383 + 2253.

A cubic polynomial :
(X + 15042)(X + 26882)(X + 38072) = X3 + 48972X2 + 124034882X + 153907568642.

Page of Squares : First Upload July 23, 2007 ; Last Revised December 29, 2013
by Yoshio Mimura, Kobe, Japan

3808

38082± 3 are primes.

38082 = 813 + 1183 + 2313.

Page of Squares : First Upload August 22, 2008 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

3809

A cubic polynomial :
(X + 6282)(X + 11042)(X + 35912) = X3 + 38092X2 + 46133882X + 24896833922.

Page of Squares : First Upload July 23, 2007 ; Last Revised July 23, 2007
by Yoshio Mimura, Kobe, Japan

3811

38112 = 14523721, 1 * 45 * 2 + 3721 = 3811.

Page of Squares : First Upload July 23, 2007 ; Last Revised July 23, 2007
by Yoshio Mimura, Kobe, Japan

3812

38122 = 15 + 45 + 155 + 185 + 265.

1 / 3812 = 0.00026232948583, 22 + 62 + 232 + 292 + 482 + 52 + 82 + 32 = 3812.

Page of Squares : First Upload July 23, 2007 ; Last Revised August 22, 2008
by Yoshio Mimura, Kobe, Japan

3816

38164 = 212047650164736,
and 22 + 122 + 02 + 42 + 72 + 62 + 52 + 02 + 12 + 62 + 472 + 362 = 3816,
and 22 + 122 + 02 + 472 + 62 + 52 + 02 + 12 + 62 + 42 + 72 + 362 = 3816.

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

3817

38172 = 14569489, 1 + 456 * 9 - 4 * 8 * 9 = 3817.

1265k + 1529k + 3817k + 5489k are squares for k = 1,2,3 (1102, 69742, 4760142).

Page of Squares : First Upload July 23, 2007 ; Last Revised June 7, 2011
by Yoshio Mimura, Kobe, Japan

3819

38192 = 14584761, 1 + 4 + 5 + 8 * 476 + 1 = 3819.

Page of Squares : First Upload July 23, 2007 ; Last Revised July 23, 2007
by Yoshio Mimura, Kobe, Japan

3821

1 / 3821 = 0.000261711593, 22 + 62 + 172 + 12 + 12 + 592 + 32 = 3821.

Page of Squares : First Upload July 23, 2007 ; Last Revised July 23, 2007
by Yoshio Mimura, Kobe, Japan

3822

38222 = (12 + 3)(62 + 3)(3062 + 3) = (22 + 3)(62 + 3)(122 + 3)(192 + 3).

Page of Squares : First Upload December 21, 2013 ; Last Revised December 21, 2013
by Yoshio Mimura, Kobe, Japan

3824

38243 = 55918260224, and 52 + 52 + 92 + 12 + 82 + 22 + 602 + 22 + 22 + 42 = 3824.

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

3825

38252 = (42 + 9)(62 + 9)(1142 + 9) = (62 + 9)(122 + 9)(462 + 9).

38252 = 104 + 204 + 354 + 604 = 154 + 304 + 304 + 604.

Page of Squares : First Upload August 22, 2008 ; Last Revised December 21, 2013
by Yoshio Mimura, Kobe, Japan

3828

38282 = 1253 + 1303 + 2193.

Page of Squares : First Upload August 22, 2008 ; Last Revised August 22, 2008
by Yoshio Mimura, Kobe, Japan

3829

38292 = 423 + 1133 + 2363.

Page of Squares : First Upload August 22, 2008 ; Last Revised August 22, 2008
by Yoshio Mimura, Kobe, Japan

3830

38305 = 824126482214300000 : 82 + 22 + 42 + 12 + 22 + 62 + 482 + 222 + 12 + 42 + 302 + 02 + 02 + 02 + 02 = 3830.

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

3834

38342 = 873 + 903 + 2373.

38342 = 14699556, 14 + 6 / 9 * 955 * 6 = 146 * 9 + 9 * 5 * 56 = 3834.

38345 = 828439013253419424 : 82 + 22 + 82 + 432 + 92 + 02 + 132 + 252 + 32 + 42 + 192 + 42 + 242 = 82 + 282 + 42 + 32 + 92 + 02 + 12 + 322 + 52 + 342 + 12 + 92 + 42 + 242 = 3834.

Page of Squares : First Upload July 23, 2007 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

3835

1 / 3835 = 0.0002607561, 22 + 62 + 02 + 72 + 52 + 612 = 3835,
1 / 3835 = 0.0002607561, 22 + 62 + 072 + 52 + 612 = 3835.

Page of Squares : First Upload July 23, 2007 ; Last Revised July 23, 2007
by Yoshio Mimura, Kobe, Japan

3837

38374 = 216754037959761, and 22 + 12 + 62 + 72 + 52 + 42 + 02 + 32 + 72 + 92 + 592 + 72 + 62 + 12 = 3827.

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

3838

513k + 1292k + 3382k + 3838k are squares for k = 1,2,3 (952, 53012, 3122652).

Page of Squares : First Upload June 7, 2011 ; Last Revised June 7, 2011
by Yoshio Mimura, Kobe, Japan

3839

38392 = 983 + 1343 + 2253.

38392 = 14737921, 1 + 47 + 3792 - 1 = 1 * 47 + 3792 * 1 = 3839.

Page of Squares : First Upload July 23, 2007 ; Last Revised August 22, 2008
by Yoshio Mimura, Kobe, Japan

3840

682 + 3840 = 922, 682 - 3840 = 282.

38402 = (32 - 1)(52 - 1)(92 - 1)(312 - 1).

Page of Squares : First Upload July 27, 2011 ; Last Revised December 21, 2013
by Yoshio Mimura, Kobe, Japan

3841

38412 = 14753281, 12 + 42 + 72 + 52 + 32 + 22 + 82 + 12 = 132.

Page of Squares : First Upload July 23, 2007 ; Last Revised July 23, 2007
by Yoshio Mimura, Kobe, Japan

3842

3842k + 26216k + 34465k + 50398k are squares for k = 1,2,3 (3392, 665572, 136755992).

Page of Squares : First Upload June 7, 2011 ; Last Revised June 7, 2011
by Yoshio Mimura, Kobe, Japan

3844

The square of 62.

38442 = 1243 + 1863 + 1863.

1 / 3844 = 0.0002601..., and 2601 = 512.

38442 = 14776336, 1 - 4 + 7 * 7 + 633 * 6 = 3844.

Page of Squares : First Upload July 23, 2007 ; Last Revised August 22, 2008
by Yoshio Mimura, Kobe, Japan

3846

38462 = 14791716, 1 + 4 + 7 + 9 * 1 * 71 * 6 = 3846.

Page of Squares : First Upload July 23, 2007 ; Last Revised July 23, 2007
by Yoshio Mimura, Kobe, Japan

3847

38472 = 414 + 444 + 444 + 464.

Page of Squares : First Upload August 22, 2008 ; Last Revised August 22, 2008
by Yoshio Mimura, Kobe, Japan

3849

38492 = 963 + 1133 + 2323.

Page of Squares : First Upload August 22, 2008 ; Last Revised August 22, 2008
by Yoshio Mimura, Kobe, Japan

3850

38502± 3 are primes.

38502 = (12 + 6)(22 + 6)(42 + 6)(72 + 6)(132 + 6) = (12 + 6)(22 + 6)(72 + 6)(622 + 6)
= (12 + 6)(42 + 6)(82 + 6)(372 + 6) = (22 + 6)(132 + 6)(922 + 6) = (42 + 6)(132 + 6)(622 + 6)
= (42 + 6)(222 + 6)(372 + 6) = (42 + 6)(72 + 6)(82 + 6)(132 + 6) = (72 + 6)(82 + 6)(622 + 6).

Page of Squares : First Upload December 21, 2013 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

3852

38522± 5 are primes.

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

3854

3854 = (12 + 22 + 32 + ... + 1642) / (12 + 22 + 32 + ... + 102).

38542 = S2(21) + S2(354), where S2(n) = 12 + 22 + 32 + 42 + ... + n2.

38542 = 5392 + 5402 + 5412 + 5422 + 5432 + 5442 + ... + 5852.

Page of Squares : First Upload July 23, 2007 ; Last Revised November 25, 2008
by Yoshio Mimura, Kobe, Japan

3856

38562 = 873 + 1163 + 2333.

Page of Squares : First Upload August 22, 2008 ; Last Revised August 22, 2008
by Yoshio Mimura, Kobe, Japan

3860

38602± 3 are primes.

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

3861

38614 = 222228219397041, and 222 + 222 + 282 + 212 + 92 + 392 + 72 + 02 + 42 + 12 = 3861.

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

3862

38622 = 14 + 314 + 374 + 594.

1 / 3862 = 0.00025893319523, 252 + 82 + 92 + 32 + 32 + 192 + 522 + 32 = 3862.

Page of Squares : First Upload July 23, 2007 ; Last Revised August 22, 2008
by Yoshio Mimura, Kobe, Japan

3864

38642 = 1913 + 245 + 17.

Page of Squares : First Upload October 4, 2010 ; Last Revised October 4, 2010
by Yoshio Mimura, Kobe, Japan

3865

The quadratic polynomial 3865X2 - 15750X + 33201 takes the values 1462, 1312, 1442, 1792, 2262, 2792 at X = 1, 2,..., 6,

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

3868

1 / 3868 = 0.000258531540847, 252 + 82 + 532 + 152 + 42 + 082 + 42 + 72 = 3868.

Page of Squares : First Upload July 23, 2007 ; Last Revised July 23, 2007
by Yoshio Mimura, Kobe, Japan

3869

38692 = 14969161, 1 + 4 * 969 - 1 - 6 - 1 = 1 * 4 * 969 - 1 - 6 * 1 = 3869,
  = 1 * 4 * 969 - 1 * 6 - 1 = 1 * 4 * 969 * 1 - 6 - 1 = 3869.

3869 = 622+ 052 and 6205 = 382 + 692.

Page of Squares : First Upload July 23, 2007 ; Last Revised October 9, 2008
by Yoshio Mimura, Kobe, Japan

3870

38702 = (227 + 228 + 229)2 + (230 + 231 + 232)2 + (233 + 234 + 235)2 + ... + (296 + 297 + 298)2.

Page of Squares : First Upload July 23, 2007 ; Last Revised July 23, 2007
by Yoshio Mimura, Kobe, Japan

3871

38712 = 14984641, 1 * 4 * 984 - 64 - 1 = 1 + 49 * 84 - 6 * 41 = 3871.

Page of Squares : First Upload July 23, 2007 ; Last Revised July 23, 2007
by Yoshio Mimura, Kobe, Japan

3872

38722 = 444 + 444 + 444 + 444.

38722 = 14992384, 1 * 4 * 992 - 3 * 8 * 4 = 3872.

38722 = (12 + 7)(22 + 7)(132 + 7)(312 + 7) = (22 + 7)(32 + 7)(92 + 7)(312 + 7)
= (92 + 7)(132 + 7)(312 + 7).

Page of Squares : First Upload July 23, 2007 ; Last Revised December 21, 2013
by Yoshio Mimura, Kobe, Japan

3873

38732± 2 are primes.

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

3875

1 / 3875 = 0.000258064..., and 258064 = 5082.

Page of Squares : First Upload July 23, 2007 ; Last Revised July 23, 2007
by Yoshio Mimura, Kobe, Japan

3876

The integral triangle of sides 361, 104040, 104257 has square area 38762.

Page of Squares : First Upload October 11, 2011 ; Last Revised October 11, 2011
by Yoshio Mimura, Kobe, Japan

3878

Loop of length 56 by the function f(N) = ... + c2 + b2 + a2 where N = ... + 1002c + 100b + a:
3878 - 7528 - 6409 - 4177 - ... - 7251 - 7785 - 13154 - 3878
(Note f(3878) = 382 + 782 = 7528,   f(7528) = 752 + 282 = 6409, etc. See 41)

The square root of 3878 is 62.273..., and 62 = 22 + 72 + 32.

Page of Squares : First Upload July 23, 2007 ; Last Revised October 9, 2008
by Yoshio Mimura, Kobe, Japan

3879

38792± 2 are primes.

38792 = 463 + 1323 + 2333.

Page of Squares : First Upload August 22, 2008 ; Last Revised December 29, 2013
by Yoshio Mimura, Kobe, Japan

3880

38802 = 993 + 215 + 107.

Page of Squares : First Upload October 4, 2010 ; Last Revised October 4, 2010
by Yoshio Mimura, Kobe, Japan

3882

38822 = 15069924, 1506 + 99 * 24 = 3882.

786k + 1614k + 3882k + 4122k are squares for k = 1,2,3 (1022, 59402, 3650042).

Page of Squares : First Upload July 23, 2007 ; Last Revised June 7, 2011
by Yoshio Mimura, Kobe, Japan

3884

38842 = 1283 + 1383 + 2183.

Page of Squares : First Upload August 22, 2008 ; Last Revised August 22, 2008
by Yoshio Mimura, Kobe, Japan

3886

38862 = 15100996, and 12 + 52 + 12 + 02 + 02 + 92 + 92 + 62 = 152.

Page of Squares : First Upload July 23, 2007 ; Last Revised July 23, 2007
by Yoshio Mimura, Kobe, Japan

3887

38872 = 134 + 264 + 524 + 524 = 15 + 35 + 35 + 155 + 275.

Page of Squares : First Upload August 22, 2008 ; Last Revised August 22, 2008
by Yoshio Mimura, Kobe, Japan

3888

38882 = (12 + 8)(22 + 8)(82 + 8)(442 + 8) = (82 + 8)(102 + 8)(442 + 8).

38882 = 35 + 35 + 65 + 155 + 275.

A cubic polynomial :
(X + 35842)(X + 38882)(X + 160232) = X3 + 168732X2 + 858658082X + 223273967616.

Komachi equation: 38882 = - 122 * 32 * 452 + 62 * 782 * 92.

38882 = 15116544, and 12 + 52 + 12 + 12 + 62 + 52 + 42 + 42 = 112.

Page of Squares : First Upload December 21, 2013 ; Last Revised December 21, 2013
by Yoshio Mimura, Kobe, Japan

3892

1 / x = 0.000256..., and 256 = 162 for x = 3892, 3893,..., 3906.

Page of Squares : First Upload July 23, 2007 ; Last Revised July 23, 2007
by Yoshio Mimura, Kobe, Japan

3894

38942 = 15163236, and 12 + 52 + 12 + 62 + 32 + 22 + 32 + 62 = 112.

Page of Squares : First Upload July 23, 2007 ; Last Revised July 23, 2007
by Yoshio Mimura, Kobe, Japan

3896

38962 = 603 + 1143 + 2383.

38962 = 15178816, and 15 - 1 * 7 + 8 * 81 * 6 = 15 * 1 - 7 + 8 * 81 * 6 = 3896.

Page of Squares : First Upload July 23, 2007 ; Last Revised August 22, 2008
by Yoshio Mimura, Kobe, Japan

3897

38972 = 64 + 424 + 484 + 514.

Page of Squares : First Upload August 22, 2008 ; Last Revised August 22, 2008
by Yoshio Mimura, Kobe, Japan

3898

1 / 3898 = 0.000256541816, 252 + 62 + 542 + 12 + 82 + 162 = 3898.

Page of Squares : First Upload July 23, 2007 ; Last Revised July 23, 2007
by Yoshio Mimura, Kobe, Japan