3901
517k + 893k + 3525k + 3901k are squares for k = 1,2,3 (942, 53582, 3225142).
Page of Squares : First Upload June 7, 2011 ; Last Revised June 7, 2011by Yoshio Mimura, Kobe, Japan
3903
39032 = 24 + 34 + 264 + 624 = 44 + 84 + 424 + 594.
Page of Squares : First Upload August 22, 2008 ; Last Revised August 22, 2008by Yoshio Mimura, Kobe, Japan
3904
39042 = 15241216, a zigzag square.
Page of Squares : First Upload July 30, 2007 ; Last Revised July 30, 2007by Yoshio Mimura, Kobe, Japan
3907
39072 = 15264649, a zigzag square.
(39072 + 8) = (32 + 8)(72 + 8)(92 + 8)(132 + 8).
Page of Squares : First Upload July 30, 2007 ; Last Revised July 30, 2007by Yoshio Mimura, Kobe, Japan
3908
39084 = 233248156631296, and 22 + 32 + 322 + 482 + 152 + 62 + 62 + 32 + 122 + 92 + 62 = 3908.
Page of Squares : First Upload December 1, 2008 ; Last Revised December 1, 2008by Yoshio Mimura, Kobe, Japan
3911
3911 is the 10th prime for which the Legendre symbol (a/3911) = 1 for a = 1,2,...,12.
Page of Squares : First Upload July 30, 2007 ; Last Revised July 30, 2007by Yoshio Mimura, Kobe, Japan
3912
39122 = 163 + 363 + 2483.
Page of Squares : First Upload August 22, 2008 ; Last Revised August 22, 2008by Yoshio Mimura, Kobe, Japan
3914
39142 = 15319396, a square with odd digits except the last digit 6.
The square root of 3914 is 62.561..., and 62 = 52 + 62 + 12.
Page of Squares : First Upload July 30, 2007 ; Last Revised August 24, 2013by Yoshio Mimura, Kobe, Japan
3915
39152 = 15327225, and 12 + 52 + 32 + 22 + 72 + 22 + 22 + 52 = 112.
Komachi equations:
39152 = 92 * 872 * 62 * 52 / 42 / 32 * 22 */ 12 = 92 * 872 / 62 * 52 * 42 * 32 / 22 */ 12.
by Yoshio Mimura, Kobe, Japan
3916
39162± 3 are primes.
39162 + 39172 + 39182 + ... + 39602 = 39612 + 39622 + 39632 + ... + 40042.
Page of Squares : First Upload September 13, 2011 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
3918
39182 = 15350724, a zigzag square.
Page of Squares : First Upload July 30, 2007 ; Last Revised July 30, 2007by Yoshio Mimura, Kobe, Japan
3920
Komachi equation: 39202 = 92 * 82 * 72 * 62 / 542 / 32 * 2102.
Page of Squares : First Upload October 8, 2010 ; Last Revised October 8, 2010by Yoshio Mimura, Kobe, Japan
3921
39212 = 343 + 1583 + 2253 = 1083 + 1373 + 2263.
39212 = 15374241, and 12 + 52 + 32 + 72 + 42 + 22 + 42 + 12 = 112.
39212 = 15374241 , 1 + 53 * 74 + 2 - 4 * 1 = 1 * 53 * 74 + 2 - 4 + 1 = 3921.
Page of Squares : First Upload July 30, 2007 ; Last Revised August 22, 2008by Yoshio Mimura, Kobe, Japan
3923
39232 = 15389929, 1 + 5 + 3899 + 2 * 9 = 3923.
Page of Squares : First Upload July 30, 2007 ; Last Revised July 30, 2007by Yoshio Mimura, Kobe, Japan
3924
39242 = 15397776, a square with odd digits except the last digit 6.
Page of Squares : First Upload August 24, 2013 ; Last Revised August 24, 2013by Yoshio Mimura, Kobe, Japan
3925
39252 = 13 - 23 + 33 - 43 + 53 - 63 + ... + 3113 - 3123 + 3133.
39252 = 15405625, and 1 = 12, 5405625 = 23252.
Page of Squares : First Upload July 30, 2007 ; Last Revised July 30, 2007by Yoshio Mimura, Kobe, Japan
3926
1 / 3926 = 0.00025471217524, 252 + 472 + 12 + 212 + 72 + 52 + 242 = 3926.
Page of Squares : First Upload July 30, 2007 ; Last Revised July 30, 2007by Yoshio Mimura, Kobe, Japan
3928
39282± 3 are primes.
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
3930
2460k + 2490k + 3930k + 9345k are squares for k = 1,2,3 (1352, 107252, 9524252).
Page of Squares : First Upload June 7, 2011 ; Last Revised June 7, 2011by Yoshio Mimura, Kobe, Japan
3932
39322 = 15460624, a zigzag square.
39322 = 613 + 963 + 2433 = 623 + 1663 + 2203 = 84 + 164 + 284 + 624 = 124 + 244 + 244 + 624.
Page of Squares : First Upload July 30, 2007 ; Last Revised August 22, 2008by Yoshio Mimura, Kobe, Japan
3933
39335 = 941065239592294893 : 92 + 42 + 102 + 62 + 52 + 232 + 92 + 52 + 92 + 222 + 92 + 482 + 92 + 32 = 3933.
Page of Squares : First Upload December 8, 2007 ; Last Revised December 8, 2008by Yoshio Mimura, Kobe, Japan
3934
39342 = 773 + 793 + 2443.
39342 = 15476356, and 154 + 7 * 6 * 3 * 5 * 6 = 3934.
Page of Squares : First Upload July 30, 2007 ; Last Revised August 22, 2008by Yoshio Mimura, Kobe, Japan
3937
49k + 98k + 170k + 212k are squares for k = 1,2,3 (232, 2932, 39372).
Page of Squares : First Upload June 7, 2011 ; Last Revised June 7, 2011by Yoshio Mimura, Kobe, Japan
3938
39382 = 15507844, and 12 + 52 + 52 + 02 + 72 + 82 + 42 + 42 = 142.
39382 = 15507844, 1 * 550 * 7 + 84 + 4 = 3938.
Page of Squares : First Upload July 30, 2007 ; Last Revised July 30, 2007by Yoshio Mimura, Kobe, Japan
3942
39422 = 15539364, 1 + 5 / 5 + 3936 + 4 = 1 * 5 + 5 + 3936 - 4 = 15 - 5 + 3936 - 4 = 3942.
39424 = 241471833524496, and 242 + 142 + 72 + 12 + 82 + 32 + 32 + 52 + 242 + 492 + 62 = 3942.
39425 = 951881967753563232, and 92 + 512 + 82 + 82 + 192 + 62 + 72 + 72 + 52 + 32 + 52 + 62 + 32 + 232 + 22 = 3942.
Page of Squares : First Upload July 30, 2007 ; Last Revised December 8, 2008by Yoshio Mimura, Kobe, Japan
3943
39432 = 15547249, 1 + 5 + 54 * 72 + 49 = 3943.
Page of Squares : First Upload July 30, 2007 ; Last Revised July 30, 2007by Yoshio Mimura, Kobe, Japan
3944
39442 = 15555136, a square with odd digits except the last digit 6.
Page of Squares : First Upload July 30, 2007 ; Last Revised August 24, 2013by Yoshio Mimura, Kobe, Japan
3945
Komachi equations:
39452 = 12 * 22 / 32 / 42 * 52 * 62 * 7892 = 12 / 22 * 32 * 42 * 52 / 62 * 7892
= 12 * 22 / 32 * 452 / 62 * 7892.
by Yoshio Mimura, Kobe, Japan
3950
39502 = (98 + 99 + 100 + 101 + 102)2 + (103 + 104 + 105 + 106 + 107)2 + (108 + 109 + 110 + 111 + 112)2 + ... + (213 + 214 + 215 + 216 + 217)2.
Page of Squares : First Upload July 30, 2007 ; Last Revised July 30, 2007by Yoshio Mimura, Kobe, Japan
3951
39512 = 1343 + 1443 + 2173.
Page of Squares : First Upload August 22, 2008 ; Last Revised August 22, 2008by Yoshio Mimura, Kobe, Japan
3952
39522± 3 are primes.
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
3953
39532 = 294 + 344 + 444 + 564.
39532 = 1032 + 1052 + 1072 + 1092 + 1112 + 1132 + ... + 4552.
Page of Squares : First Upload July 30, 2007 ; Last Revised August 22, 2008by Yoshio Mimura, Kobe, Japan
3954
39542 = 15634116, 1 * 5 * 6 * 3 * 4 * 11 - 6 = 3954.
Page of Squares : First Upload July 30, 2007 ; Last Revised July 30, 2007by Yoshio Mimura, Kobe, Japan
3955
1 / 3955 = 0.00025284450063211, 22 + 52 + 282 + 442 + 52 + 0062 + 322 + 112 = 3955.
39552 = (393 + 394 + 395 + 396 + 397 + 398 + 399)2 + (400 + 401 + 402 + 403 + 404 + 405 + 406)2 + (407 + 408 + 409 + 410 + 411 + 412 + 413)2 + ... + (400 + 401 + 402 + 403 + 404 + 405 + 406)2.
Page of Squares : First Upload July 30, 2007 ; Last Revised July 30, 2007by Yoshio Mimura, Kobe, Japan
3956
39562 = 15649936, 1 - 5 - 6 + 4 * 993 - 6 = 3956.
Page of Squares : First Upload July 30, 2007 ; Last Revised July 30, 2007by Yoshio Mimura, Kobe, Japan
3958
39582 = 15665764, 1 + 5 + 6 + 657 * 6 + 4 = 1 + 5 + 6 * 657 + 6 + 4 = 3958.
Page of Squares : First Upload July 30, 2007 ; Last Revised July 30, 2007by Yoshio Mimura, Kobe, Japan
3960
39602 = 123 + 383 + 2503.
39602= 9 x 10 + 10 x 11 + 11 x 12 +...+ 360 x 361.
343 + 3960 = 2082, 343 - 3960 = 1882,
1012 + 3960 = 1192, 1012 - 3960 = 792.
39602 = (179 + 180 + 181)2 + (182 + 183 + 184)2 + (185 + 186 + 187)2 + (188 + 189 + 190)2 + ... + (275 + 276 + 277)2.
39602 = (102 - 1)(192 - 1)(212 - 1) = (22 - 1)(102 - 1)(112 - 1)(212 - 1) = (22 - 1)(212 - 1)(1092 - 1) = (22 - 1)(32 - 1)(42 - 1)(102 - 1)(212 - 1) = (42 - 1)(52 - 1)(102 - 1)(212 - 1).
Page of Squares : First Upload July 30, 2007 ; Last Revised December 21, 2013by Yoshio Mimura, Kobe, Japan
3963
1 / 3963 = 0.0002523340903, 22 + 522 + 32 + 342 + 02 + 92 + 02 + 32 = 3963,
1 / 3963 = 0.0002523340903, 22 + 522 + 32 + 342 + 02 + 92 + 032 = 3963,
1 / 3963 = 0.0002523340903, 22 + 522 + 32 + 342 + 092 + 02 + 32 = 3963,
1 / 3963 = 0.0002523340903, 22 + 522 + 32 + 342 + 092 + 032 = 3963.
by Yoshio Mimura, Kobe, Japan
3969
The square of 63.
39692 = 503 + 1293 + 2383 = 633 + 1473 + 2313.
Komachi equations:
39692 = 122 * 32 / 42 * 562 * 72 / 82 * 92,
39692 = 94 * 84 * 74 * 64 * 54 / 44 / 34 / 24 / 104 = 94 * 84 * 74 / 64 * 54 / 44 * 34 * 24 / 104
= 94 * 84 * 74 / 64 / 54 / 44 * 34 / 24 * 104 = 94 / 84 * 74 * 64 * 54 * 44 / 34 * 24 / 104
= 94 / 84 * 74 * 64 / 54 * 44 / 34 / 24 * 104 = 94 / 84 * 74 / 64 / 54 * 44 * 34 * 24 * 104
= 984 / 74 * 64 * 54 / 44 * 34 * 24 / 104 = 984 / 74 * 64 / 54 / 44 * 34 / 24 * 104.
by Yoshio Mimura, Kobe, Japan
3970
39702 = 1423 + 1813 + 1913.
730k + 3970k + 4190k + 8010k are squares for k = 1,2,3 (1302, 99002, 8065002).
Page of Squares : First Upload August 22, 2008 ; Last Revised June 7, 2011by Yoshio Mimura, Kobe, Japan
3971
39712 = 15768841,and 12 + 52 + 72 + 62 + 82 + 82 + 42 + 12 = 162.
39712 = 6592 + 6612 + 6632 + 6652 + 6672 + 6692 + ... + 7232.
Page of Squares : First Upload July 30, 2007 ; Last Revised July 30, 2007by Yoshio Mimura, Kobe, Japan
3972
39722 = 184 + 324 + 524 + 524 = 15 + 35 + 65 + 175 + 275.
39722 = 15776784, and 12 + 52 + 72 + 72 + 62 + 72 + 82 + 42 = 172.
39722 = 15776784, 1 + 5 * 776 + 7 + 84 = 3972.
Page of Squares : First Upload July 30, 2007 ; Last Revised August 22, 2008by Yoshio Mimura, Kobe, Japan
3973
39732 = 15784729, and 12 + 52 + 72 + 82 + 42 + 72 + 22 + 92 = 172.
Page of Squares : First Upload July 30, 2007 ; Last Revised July 30, 2007by Yoshio Mimura, Kobe, Japan
3975
39752 = 323 + 1693 + 2223.
Page of Squares : First Upload August 22, 2008 ; Last Revised August 22, 2008by Yoshio Mimura, Kobe, Japan
3976
39762 = (72 + 7)(82 + 7)(632 + 7).
Page of Squares : First Upload December 21, 2013 ; Last Revised December 21, 2013by Yoshio Mimura, Kobe, Japan
3978
39782 = (22 + 9)(52 + 9)(122 + 9)(152 + 9).
Page of Squares : First Upload December 21, 2013 ; Last Revised December 21, 2013by Yoshio Mimura, Kobe, Japan
3984
39842 = 743 + 1183 + 2403 = 1003 + 1203 + 2363.
Page of Squares : First Upload August 22, 2008 ; Last Revised August 22, 2008by Yoshio Mimura, Kobe, Japan
3988
39882 = 1383 + 1383 + 2203.
The square root of 3988 is 63.15061..., and 63 = 12 + 52 + 02 + 62 + 12.
39885 = 1008731883934471168 : 12 + 02 + 02 + 82 + 72 + 32 + 12 + 82 + 82 + 392 + 32 + 442 + 72 + 112 + 62 + 82 = 3988.
Page of Squares : First Upload July 30, 2007 ; Last Revised December 8, 2008by Yoshio Mimura, Kobe, Japan
3989
Loop of length 35 by the function f(N) = ... + c2 + b2 + a2 where N = ... + 1002c + 100b + a:
3989 - 9442 - 10600 - 37 - ... - 8685 - 14621 - 2558 - 3989
(Note f(3989) = 392 + 892 = 9442, f(9442) = 942 + 422 = 10600, etc. See 37)
by Yoshio Mimura, Kobe, Japan
3990
39902 = 353 + 763 + 2493.
The integral triangle of sides 861, 37405, 37544 (or 9386, 10955, 20091) has square area 39902.
Page of Squares : First Upload August 22, 2008 ; Last Revised October 11, 2011by Yoshio Mimura, Kobe, Japan
3993
39932 = 1213 + 2423.
Page of Squares : First Upload August 22, 2008 ; Last Revised August 22, 2008by Yoshio Mimura, Kobe, Japan
3996
39962± 5 are primes.
39962 = 15968016, 1 * 59 * 68 + 0 - 16 = 1 * 59 * 68 - 16 = 3996.
Page of Squares : First Upload July 30, 2007 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
3997
39972 = 353 + 1873 + 2113.
154k + 490k + 1708k + 3577k are squares for k = 1,2,3 (772, 39972, 2255472).
Page of Squares : First Upload August 22, 2008 ; Last Revised June 7, 2011by Yoshio Mimura, Kobe, Japan