4000
40002 = 2003 + 2003 = 205 + 205 + 205 + 205 + 205.
400040001 = 200012.
Page of Squares : First Upload August 6, 2007 ; Last Revised August 26, 2008by Yoshio Mimura, Kobe, Japan
4002
40022± 5 are primes.
40022 = 74 + 194 + 194 + 634.
Page of Squares : First Upload August 26, 2008 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
4004
40045 = 1029130250245121024 : 102 + 22 + 92 + 12 + 302 + 252 + 02 + 22 + 452 + 122 + 102 + 22 + 42 = 4004.
2080k + 3497k + 4004k + 4108k are squares for k = 1,2,3 (1172, 70332, 4304432).
Page of Squares : First Upload December 8, 2008 ; Last Revised June 7, 2011by Yoshio Mimura, Kobe, Japan
4007
40072 = 344 + 464 + 464 + 494.
40075 = 1032991414928036807 :
102 + 322 + 92 + 92 + 12 + 412 + 42 + 92 + 282 + 02 + 32 + 62 + 82 + 02 + 72 = 4007.
by Yoshio Mimura, Kobe, Japan
4011
40112 = 413 + 1963 + 2043.
The square root of 4011 is 63.33245..., and 63 = 32 + 32 + 22 + 42 + 52.
Page of Squares : First Upload August 6, 2007 ; Last Revised August 26, 2008by Yoshio Mimura, Kobe, Japan
4016
40163 = 64771076096, and 62 + 42 + 72 + 72 + 102 + 72 + 602 + 92 + 62 = 4016.
Page of Squares : First Upload December 1, 2008 ; Last Revised December 1, 2008by Yoshio Mimura, Kobe, Japan
4017
S2(4017) = S2(3076) + S2(3293), where S2(n) = 12 + 22 + 32 + 42 + 52 + ... + n2.
40172 = 272 + 282 + 292 + 302 + 312 + ... + 3642.
Page of Squares : First Upload August 6, 2007 ; Last Revised August 6, 2007by Yoshio Mimura, Kobe, Japan
4018
40182 = 74 + 214 + 214 + 634 = 174 + 234 + 534 + 534.
Page of Squares : First Upload August 26, 2008 ; Last Revised August 26, 2008by Yoshio Mimura, Kobe, Japan
4020
Komachi equations:
40202 = 12 * 23452 / 62 / 72 * 82 * 92 = 12 * 22 / 32 / 42 * 52 * 672 * 82 * 92
= 12 / 22 * 32 * 452 * 672 * 82 / 92.
by Yoshio Mimura, Kobe, Japan
4022
40222± 3 are primes.
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
4023
40232 = 16184529, a zigzag square.
Page of Squares : First Upload August 6, 2007 ; Last Revised August 6, 2007by Yoshio Mimura, Kobe, Japan
4024
40242 = 1003 + 1623 + 2223.
Page of Squares : First Upload August 26, 2008 ; Last Revised August 26, 2008by Yoshio Mimura, Kobe, Japan
4026
330k + 1353k + 4026k + 4092k are squares for k = 1,2,3 (992, 59072, 3691712).
Page of Squares : First Upload June 7, 2011 ; Last Revised June 7, 2011by Yoshio Mimura, Kobe, Japan
4027
40272 = 16216729, 1 - 6 + 2 * 16 * 7 * 2 * 9 = 4027.
Page of Squares : First Upload August 6, 2007 ; Last Revised August 6, 2007by Yoshio Mimura, Kobe, Japan
4028
40282 = 16224784, 1 * 6 / 2 * 24 * 7 * 8 - 4 = 4028.
Page of Squares : First Upload August 6, 2007 ; Last Revised August 6, 2007by Yoshio Mimura, Kobe, Japan
4031
40312 = 813 + 943 + 2463.
40312 = 16248961, 1 * 624 * 8 - 961 = 4031.
Page of Squares : First Upload August 6, 2007 ; Last Revised August 26, 2008by Yoshio Mimura, Kobe, Japan
4032
40322 = 1203 + 1743 + 2103 = 164 + 324 + 484 + 564 = 244 + 484 + 484 + 484 = 105 + 145 + 145 + 205 + 265.
40322 = 16257024, 1 * 6 * 2 / 5 * 70 * 24 = 4032.
40322 = (22 - 1)(32 - 1)(152 - 1)(552 - 1) = (22 - 1)(32 - 1)(72 - 1)(82 - 1)(152 - 1)
= (52 - 1)(152 - 1)(552 - 1) = (52 - 1)(72 - 1)(82 - 1)(152 - 1) = (43 + 8)(63 + 8)(103 + 8).
Komachi equations:
40322 = 122 * 34562 * 72 / 82 / 92 = 982 / 72 / 62 * 542 * 322 */ 12
= 92 * 82 * 72 * 62 * 52 * 42 / 32 * 22 / 102 = 92 * 82 * 72 * 62 / 52 * 42 / 32 / 22 * 102
= 92 * 82 * 72 / 62 / 52 * 42 * 32 * 22 * 102 = 982 / 72 * 62 / 52 * 42 * 32 * 22 * 102.
by Yoshio Mimura, Kobe, Japan
4039
S2(4039) = S2(580) + S2(4035), where S2(n) = 12 + 22 + 32 + 42 + 52 + ... + n2.
40392 = S2(265) + S2(311).
Page of Squares : First Upload August 6, 2007 ; Last Revised August 6, 2007by Yoshio Mimura, Kobe, Japan
4040
40402 = 723 + 1603 + 2283 = 743 + 1693 + 2233 = 1243 + 1773 + 2073.
Page of Squares : First Upload August 26, 2008 ; Last Revised August 26, 2008by Yoshio Mimura, Kobe, Japan
4042
1505k + 4042k + 4988k + 6106k are squares for k = 1,2,3 (1292, 89872, 6489992).
Page of Squares : First Upload June 7, 2011 ; Last Revised June 7, 2011by Yoshio Mimura, Kobe, Japan
4044
40442 = 16353936, a zigzag square.
Page of Squares : First Upload August 6, 2007 ; Last Revised August 6, 2007by Yoshio Mimura, Kobe, Japan
4045
40454 = 267715862100625, and 22 + 62 + 72 + 72 + 12 + 582 + 62 + 212 + 02 + 02 + 62 + 22 + 52 = 4045.
Page of Squares : First Upload December 1, 2008 ; Last Revised December 1, 2008by Yoshio Mimura, Kobe, Japan
4047
40472 = 16378209, a square with different digits.
Page of Squares : First Upload August 6, 2007 ; Last Revised August 6, 2007by Yoshio Mimura, Kobe, Japan
4048
40482 = (192 + 7)(2112 + 7) = (22 + 7)(42 + 7)(132 + 7)(192 + 7) = (22 + 7)(42 + 7)(92 + 7)(272 + 7)
= (32 + 7)(42 + 7)(2112 + 7) = (42 + 7)(272 + 7)(312 + 7).
A cubic polynomial :
(X + 7562)(X + 40482)(X + 284972) = X3 + 287932X2 + 1173902522X + 872090271362.
by Yoshio Mimura, Kobe, Japan
4049
40492 = 643 + 1683 + 2253.
Page of Squares : First Upload August 26, 2008 ; Last Revised August 26, 2008by Yoshio Mimura, Kobe, Japan
4050
40502 = 454 + 454 + 454 + 454.
Page of Squares : First Upload August 26, 2008 ; Last Revised August 26, 2008by Yoshio Mimura, Kobe, Japan
4054
40542 = 16434916, and 12 + 62 + 42 + 32 + 42 + 92 + 12 + 62 = 142.
Page of Squares : First Upload August 6, 2007 ; Last Revised August 6, 2007by Yoshio Mimura, Kobe, Japan
4056
40562 = (12 + 3)(62 + 3)(72 + 3)(452 + 3).
652 + 4056 = 912, 652 - 4056 = 132.
Page of Squares : First Upload August 2, 2011 ; Last Revised December 28, 2013by Yoshio Mimura, Kobe, Japan
4058
40582 = 16467364, 1 * 6 * 4 + 673 * 6 - 4 = 4058.
Page of Squares : First Upload August 6, 2007 ; Last Revised August 6, 2007by Yoshio Mimura, Kobe, Japan
4060
4060 = (12 + 22 + 32 + ... + 872) / (12 + 22 + 32 + 42 + 52).
40602 = 25 + 85 + 125 + 235 + 255.
S2(4060) = S2(2650) + S2(3642), where S2(n) = 12 + 22 + 32 + 42 + 52 + ... + n2.
Page of Squares : First Upload August 6, 2007 ; Last Revised November 25, 2008by Yoshio Mimura, Kobe, Japan
4062
40622± 5 are primes.
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
4063
4063 = (12 + 22 + 32 + ... + 1192) / (12 + 22 + 32 + ... + 72).
Page of Squares : First Upload November 25, 2008 ; Last Revised November 25, 2008by Yoshio Mimura, Kobe, Japan
4065
4065 = (12 + 22 + 32 + ... + 1352) / (12 + 22 + 32 + ... + 82).
Page of Squares : First Upload November 25, 2008 ; Last Revised November 25, 2008by Yoshio Mimura, Kobe, Japan
4068
40682 = 163 + 543 + 2543.
1 / 4068 = 0.0002458210422, 242 + 582 + 22 + 102 + 42 + 22 + 22 = 4068.
Page of Squares : First Upload August 6, 2007 ; Last Revised August 26, 2008by Yoshio Mimura, Kobe, Japan
4069
40692 = 16556761, 1 + 6 - 5 * 5 + 67 * 61 = 4069.
Page of Squares : First Upload August 6, 2007 ; Last Revised August 6, 2007by Yoshio Mimura, Kobe, Japan
4070
4070 = (12 + 22 + 32 + ... + 552) / (12 + 22 + 32).
40702 = S2(39) + S2(367), where S2(n) = 12 + 22 + 32 + 42 + 52 + ... + n2.
40702 = 16564900, 1 * 65 * 64 - 90 + 0 = 4070.
Page of Squares : First Upload August 6, 2007 ; Last Revised November 25, 2008by Yoshio Mimura, Kobe, Japan
4072
40722 = 224 + 224 + 344 + 624.
Page of Squares : First Upload August 26, 2008 ; Last Revised August 26, 2008by Yoshio Mimura, Kobe, Japan
4073
40732 = 274 + 424 + 424 + 564.
Page of Squares : First Upload August 26, 2008 ; Last Revised August 26, 2008by Yoshio Mimura, Kobe, Japan
4074
40742 = 16597476, 1 + 65 * 9 * 7 - 4 * 7 + 6 = 4074.
40742 = (12 + 3)(122 + 3)(1682 + 3) = 4074,(22 + 3)(92 + 3)(1682 + 3).
Page of Squares : First Upload August 6, 2007 ; Last Revised December 28, 2013by Yoshio Mimura, Kobe, Japan
4076
1 / 4076 = 0.00024533856722, 22 + 452 + 32 + 382 + 52 + 62 + 72 + 222 = 4076.
Page of Squares : First Upload August 6, 2007 ; Last Revised August 6, 2007by Yoshio Mimura, Kobe, Japan
4077
40775 = 1126428311047604157 : 112 + 262 + 422 + 82 + 312 + 102 + 42 + 72 + 62 + 02 + 42 + 152 + 72 = 4077.
Page of Squares : First Upload December 8, 2008 ; Last Revised December 8, 2008by Yoshio Mimura, Kobe, Japan
4078
69482 + 40782 = 64904788, a mosaic square.
Page of Squares : First Upload August 6, 2007 ; Last Revised August 6, 2007by Yoshio Mimura, Kobe, Japan
4082
40822 = 16662724, 1 * 66 * 62 - 7 * 2 + 4 = 4082.
Page of Squares : First Upload August 6, 2007 ; Last Revised August 6, 2007by Yoshio Mimura, Kobe, Japan
4086
4086 = (12 + 22 + 32 + ... + 5672) / (12 + 22 + 32 + ... + 352).
40862 = 873 + 1573 + 2303.
40862 = 16662724, 16 * 6 * 9 * 5 - 39 * 6 = 4086.
Page of Squares : First Upload August 6, 2007 ; Last Revised November 25, 2008by Yoshio Mimura, Kobe, Japan
4087
40872 = 253 + 1363 + 2423 = 743 + 1213 + 2443.
Page of Squares : First Upload August 26, 2008 ; Last Revised August 26, 2008by Yoshio Mimura, Kobe, Japan
4088
40882 = 16711744, 12 + 62 + 72 + 12 + 12 + 72 + 42 + 42 = 132.
40882 = 4422 + 4432 + 4442 + 4452 + 4462 + ... + 5142.
Page of Squares : First Upload August 6, 2007 ; Last Revised August 6, 2007by Yoshio Mimura, Kobe, Japan
4089
4089k + 9870k + 15792k + 25474k are squares for k = 1,2,3 (2352, 318192, 46366912).
Page of Squares : First Upload June 7, 2011 ; Last Revised June 7, 2011by Yoshio Mimura, Kobe, Japan
4092
40922 = 44 + 364 + 444 + 584.
330k + 1353k + 4026k + 4092k are squares for k = 1,2,3 (992, 59072, 3691712).
The integral triangle of sides 3330, 10057, 10571 has square area 40922.
Page of Squares : First Upload August 26, 2008 ; Last Revised October 11, 2011by Yoshio Mimura, Kobe, Japan
4094
40942± 3 are primes.
40942 = 183 + 1513 + 2373 = 1073 + 1453 + 2323.
Komachi equation: 40942 = 12 * 232 / 42 * 562 / 72 * 892.
40943 = 68618862584, and 62 + 82 + 612 + 82 + 82 + 62 + 22 + 52 + 82 + 42 = 4084.
40945 = 1150109502276960224, and 12 + 12 + 52 + 02 + 102 + 92 + 502 + 22 + 272 + 62 + 92 + 62 + 02 + 222 + 42 = 12 + 12 + 502 + 102 + 92 + 52 + 02 + 22 + 272 + 62 + 92 + 62 + 02 + 222 + 42 = 4094.
Page of Squares : First Upload August 26, 2008 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
4095
40952 = 16769025, 1 + 6 * 76 * 9 + 0 - 2 * 5 = 4095.
40952 + 40962 + 40972 + ... + 41402 = 41412 + 41422 + 41432 + ... + 41852.
Komachi equations
40952 = 92 * 82 * 72 * 652 * 42 / 322 */ 12 = 92 / 82 * 72 * 652 / 42 * 322 */ 12.
by Yoshio Mimura, Kobe, Japan
4096
The square of 64.
40962 = 93 + 583 + 2553 = 93 + 1833 + 2203 = 223 + 573 + 2553.
1 / 4096 = 0.000244140625, 244140625 = 156252.
40962 = (32 + 7)(52 + 7)(1812 + 7).
Komachi equations
40962 = 124 * 34 / 44 + 564 / 74 * 84 - 94 = 124 * 34 / 44 * 564 / 74 * 84 / 94
= - 124 * 34 / 44 + 564 / 74 * 84 + 94,
40962 = 126 * 36 * 46 * 566 / 76 / 86 / 96 = 126 * 36 * 46 / 566 * 76 * 86 / 96.
40962 = 16777216, 12 + 62 + 72 + 72 + 72 + 22 + 12 + 62 = 152.
Page of Squares : First Upload August 6, 2007 ; Last Revised December 28, 2013by Yoshio Mimura, Kobe, Japan
4097
40972 = 14 + 84 + 84 + 644 = 16 + 46 + 46 + 166.
40972 = 16785409, a square with different digits.
85k + 1649k + 4097k + 4573k are squares for k = 1,2,3 (1022, 63582, 4109582).
Page of Squares : First Upload August 6, 2007 ; Last Revised June 7, 2011by Yoshio Mimura, Kobe, Japan
4098
40982 = (12 + 5)(16732 + 5).
Page of Squares : First Upload December 28, 2013 ; Last Revised December 28, 2013by Yoshio Mimura, Kobe, Japan