3700
37002 = (12 + 1)(32 + 1)(72 + 1)(1172 + 1) = (12 + 4)(122 + 4)(1362 + 4).
37002 + 37012 + 37022 + ... + 53842 = 53852 + 53862 + 53872 + ... + 63952.
Page of Squares : First Upload September 13, 2011 ; Last Revised December 21, 2013by Yoshio Mimura, Kobe, Japan
3701
37012 = 13697401, 1 + 3697 + 4 + 0 - 1 = 1 * 3697 + 4 + 0 * 1 = 3701.
Page of Squares : First Upload July 17, 2007 ; Last Revised July 17, 2007by Yoshio Mimura, Kobe, Japan
3702
37025 = 695315758215496032 : 62 + 92 + 532 + 12 + 52 + 72 + 52 + 82 + 212 + 52 + 42 + 92 + 62 + 02 + 32 + 22 = 3702.
Page of Squares : First Upload December 8, 2008 ; Last Revised December 8, 2008by Yoshio Mimura, Kobe, Japan
3703
37032 = 234 + 464 + 464 + 464 = 344 + 444 + 444 + 474.
37032 = S2(213) + S2(315), where S2(n) = 12 + 22 + 32 + 42 + ... + n2.
37032 = 13712209, 1 * 3712 + 2 * 0 - 9 = 1 * 3712 - 2 * 0 - 9 = 3703.
Page of Squares : First Upload July 17, 2007 ; Last Revised August 18, 2008by Yoshio Mimura, Kobe, Japan
3704
37042 = 423 + 1343 + 2243 = 85 + 85 + 145 + 225 + 245.
Page of Squares : First Upload August 18, 2008 ; Last Revised August 18, 2008by Yoshio Mimura, Kobe, Japan
3708
37082 = 124 + 424 + 484 + 484.
37082 = 13749264, 1 - 37 + 4 * 9 * 26 * 4 = 3708.
Page of Squares : First Upload July 17, 2007 ; Last Revised August 18, 2008by Yoshio Mimura, Kobe, Japan
3709
37092 = 13756681, 1 + 3756 - 6 * 8 * 1 = 1 * 3756 - 6 * 8 + 1 = 3709.
Page of Squares : First Upload July 17, 2007 ; Last Revised July 17, 2007by Yoshio Mimura, Kobe, Japan
3710
37102 = (12 + 6)(22 + 6)(102 + 6)(432 + 6) = (82 + 6)(102 + 6)(432 + 6).
Page of Squares : First Upload December 21, 2013 ; Last Revised December 21, 2013by Yoshio Mimura, Kobe, Japan
3711
37112 = 713 + 1593 + 2113.
37112 = 13771521, 13 + 7 + 71 * 52 - 1 = 3711.
Page of Squares : First Upload July 17, 2007 ; Last Revised August 18, 2008by Yoshio Mimura, Kobe, Japan
3712
37122 = 1253 + 1643 + 1953.
37122 = (52 + 7)(152 + 7)(432 + 7).
Page of Squares : First Upload August 18, 2008 ; Last Revised December 21, 2013by Yoshio Mimura, Kobe, Japan
3714
37142 = 13793796, 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
3716
37162 = 403 + 1583 + 2143.
Page of Squares : First Upload August 18, 2008 ; Last Revised August 18, 2008by Yoshio Mimura, Kobe, Japan
3717
37172 = 13816089, 12 + 32 + 82 + 12 + 62 + 02 + 82 + 92 = 162.
37172 = (65 + 66 + 67)2 + (68 + 69 + 70)2 + (71 + 72 + 73)2 + ... + (239 + 240 + 241)2.
Page of Squares : First Upload July 17, 2007 ; Last Revised July 17, 2007by Yoshio Mimura, Kobe, Japan
3718
37182 = 553 + 1423 + 2213.
1 / 3718 = 0.00026896..., and 26896 = 1642.
Page of Squares : First Upload July 17, 2007 ; Last Revised August 18, 2008by Yoshio Mimura, Kobe, Japan
3721
The square of 61.
37212 = 13845841, 12 + 32 + 82 + 42 + 52 + 82 + 42 + 12 = 142.
Page of Squares : First Upload July 17, 2007 ; Last Revised July 17, 2007by Yoshio Mimura, Kobe, Japan
3722
37222 = 2273 + 95 + 87.
Page of Squares : First Upload October 4, 2010 ; Last Revised October 4, 2010by Yoshio Mimura, Kobe, Japan
3723
37232 = 13860729, a square with different digits.
37232± 2 are primes.
37232 = 303 + 1883 + 1933 = 403 + 1343 + 2253.
Page of Squares : First Upload July 17, 2007 ; Last Revised December 29, 2013by Yoshio Mimura, Kobe, Japan
3724
37242 = (22 + 3)(232 + 3)(612 + 3) = (22 + 3)(42 + 3)(52 + 3)(612 + 3) = (42 + 3)(232 + 3)(372 + 3).
37242 = S2(14) + S2(346), where S2(n) = 12 + 22 + 32 + 42 + ... + n2.
Page of Squares : First Upload July 17, 2007 ; Last Revised December 21, 2013by Yoshio Mimura, Kobe, Japan
3725
37252 = 13875625, 1 * 3875 - 6 * 25 = 3725.
Komachi equation: 37252 = 92 / 872 / 62 * 52 * 432102.
Page of Squares : First Upload July 17, 2007 ; Last Revised October 4, 2010by Yoshio Mimura, Kobe, Japan
3726
37262 = 343 + 1293 + 2273.
37262 = (12 + 5)(22 + 5)(82 + 5)(612 + 5) = (22 + 5)(72 + 5)(1692 + 5) = (72 + 5)(82 + 5)(612 + 5).
37262 = 1782 + 1792 + 1802 + 1812 + ... + 3612.
Page of Squares : First Upload July 17, 2007 ; Last Revised December 21, 2013by Yoshio Mimura, Kobe, Japan
3728
37282 = 13897984, 1 + 38 * 97 + 9 + 8 * 4 = 3728.
Page of Squares : First Upload July 17, 2007 ; Last Revised July 17, 2007by Yoshio Mimura, Kobe, Japan
3729
The square root of 3729 is 61.065..., 61 = 02 + 62 + 52.
Page of Squares : First Upload July 17, 2007 ; Last Revised July 17, 2007by Yoshio Mimura, Kobe, Japan
3732
37322 = 13 + 473 + 2403 = 663 + 1283 + 2263.
Page of Squares : First Upload August 18, 2008 ; Last Revised August 18, 2008by Yoshio Mimura, Kobe, Japan
3734
37342 = 13942756, a square with different digits.
Page of Squares : First Upload July 17, 2007 ; Last Revised July 17, 2007by Yoshio Mimura, Kobe, Japan
3738
37382 = (12 + 5)(232 + 5)(662 + 5) = (12 + 5)(42 + 5)(3332 + 5) = (112 + 5)(3332 + 5)
= (22 + 5)(32 + 5)(3332 + 5).
37382 = 1133 + 1713 + 1963.
Page of Squares : First Upload August 18, 2008 ; Last Revised December 21, 2013by Yoshio Mimura, Kobe, Japan
3740
37402 = S2(4) + S2(347), where S2(n) = 12 + 22 + 32 + 42 + ... + n2.
37405 = 731742047062400000 : 72 + 312 + 72 + 42 + 202 + 472 + 02 + 62 + 22 + 42 + 02 + 02 + 02 + 02 + 02 = 3740.
Page of Squares : First Upload July 17, 2007 ; Last Revised December 8, 2008by Yoshio Mimura, Kobe, Japan
3741
37412 + 37422 + 37432 + ... + 37842 = 37852 + 37862 + 37872 + ... + 38272.
37415 = 732720835107334701 : 72 + 32 + 272 + 202 + 82 + 352 + 12 + 02 + 72 + 32 + 342 + 72 + 02 + 12 = 3741.
Page of Squares : First Upload December 8, 2008 ; Last Revised September 13, 2011by Yoshio Mimura, Kobe, Japan
3743
37432 = 84 + 214 + 484 + 544.
Page of Squares : First Upload August 18, 2008 ; Last Revised August 18, 2008by Yoshio Mimura, Kobe, Japan
3744
37442 = (32 - 1)(252 - 1)(532 - 1) = (13 + 8)(23 + 8)(463 + 8).
Page of Squares : First Upload December 21, 2013 ; Last Revised December 21, 2013by Yoshio Mimura, Kobe, Japan
3746
37462 = 14032516, a zigzag square.
Page of Squares : First Upload July 17, 2007 ; Last Revised July 17, 2007by Yoshio Mimura, Kobe, Japan
3747
37472 = 683 + 973 + 2343.
Page of Squares : First Upload August 18, 2008 ; Last Revised August 18, 2008by Yoshio Mimura, Kobe, Japan
3748
37482 = 1163 + 1793 + 1893.
Page of Squares : First Upload August 18, 2008 ; Last Revised August 18, 2008by Yoshio Mimura, Kobe, Japan
3749
37492 = S2(207) + S2(321), S2(n) = 12 + 22 + 32 + 42 + ... + n2.
Page of Squares : First Upload July 17, 2007 ; Last Revised July 17, 2007by Yoshio Mimura, Kobe, Japan
3750
37502 = (42 + 9)(92 + 9)(792 + 9).
3750, 3751, 3752 and 3753 are four consecutive integers having square factors (the third case).
Page of Squares : First Upload November 10, 2008 ; Last Revised December 21, 2013by Yoshio Mimura, Kobe, Japan
3751
The square root of 3751 is 61.2454..., and 61 = 22 + 42 + 52 + 42.
Page of Squares : First Upload July 17, 2007 ; Last Revised July 17, 2007by Yoshio Mimura, Kobe, Japan
3753
37532 = 84 + 84 + 514 + 524 = 244 + 364 + 484 + 514.
Page of Squares : First Upload August 18, 2008 ; Last Revised August 18, 2008by Yoshio Mimura, Kobe, Japan
3754
37542 = 14092516, a zigzag square.
Page of Squares : First Upload July 17, 2007 ; Last Revised July 17, 2007by Yoshio Mimura, Kobe, Japan
3755
112 + 242 + 372 + ... + (13x+11)2 + ... + 37422 + 37552 = 369412.
Page of Squares : First Upload July 17, 2007 ; Last Revised July 17, 2007by Yoshio Mimura, Kobe, Japan
3756
37562 = 14107536, 1 + 4 - 1 + 0 + 7 * 536 = 1 * 4 + 1 * 0 + 7 * 536 = 1 * 4 - 1 * 0 + 7 * 536
= 1 * 4 * 1 + 0 + 7 * 536 = 14 - 10 + 7 * 536 = 3756.
by Yoshio Mimura, Kobe, Japan
3757
37572 = (22 + 9)(10422 + 9).
37574 = 199234608272401, and 12 + 92 + 92 + 22 + 342 + 62 + 02 + 82 + 272 + 22 + 402 + 12 =3757 .
Page of Squares : First Upload December 1, 2008 ; Last Revised December 21, 2013by Yoshio Mimura, Kobe, Japan
3758
37583 = 53072595512, and 532 + 02 + 72 + 252 + 92 + 52 + 52 + 122 = 3758.
Page of Squares : First Upload July 17, 2007 ; Last Revised December 1, 2008by Yoshio Mimura, Kobe, Japan
3762
37622 = (12 + 2)(22 + 2)(142 + 2)(632 + 2) = (12 + 2)(22 + 2)(32 + 2)(42 + 2)(632 + 2)
= (12 + 2)(32 + 2)(42 + 2)(62 + 2)(252 + 2) = (12 + 2)(32 + 2)(62 + 2)(82 + 2)(132 + 2)
= (12 + 2)(42 + 2)(82 + 2)(632 + 2) = (12 + 2)(62 + 2)(142 + 2)(252 + 2)
= (22 + 2)(62 + 2)(132 + 2)(192 + 2) = (32 + 2)(62 + 2)(132 + 2)(142 + 2)
= (32 + 2)(62 + 2)(1842 + 2) = (42 + 2)(142 + 2)(632 + 2) = (62 + 2)(192 + 2)(322 + 2).
The integral triangle of sides 369, 263177, 263530 has square area 37622.
Page of Squares : First Upload October 11, 2011 ; Last Revised December 21, 2013by Yoshio Mimura, Kobe, Japan
3764
37642 = 14167696, 12 + 42 + 12 + 62 + 72 + 62 + 92 + 62 = 162.
Page of Squares : First Upload July 17, 2007 ; Last Revised July 17, 2007by Yoshio Mimura, Kobe, Japan
3765
37652 = 14175225, 14 + 1 + 75 * 2 * 25 = 3765.
Page of Squares : First Upload July 17, 2007 ; Last Revised July 17, 2007by Yoshio Mimura, Kobe, Japan
3766
37662 = 14182756, a zigzag square.
37662 = 14182756, 12 + 42 + 12 + 82 + 22 + 72 + 52 + 62 = 142.
Page of Squares : First Upload July 17, 2007 ; Last Revised July 17, 2007by Yoshio Mimura, Kobe, Japan
3768
37682 = 14197824, a zigzag square.
Page of Squares : First Upload July 17, 2007 ; Last Revised July 17, 2007by Yoshio Mimura, Kobe, Japan
3770
37702 = (12 + 1)(22 + 1)(122 + 1)(992 + 1) = (12 + 1)(22 + 1)(172 + 1)(702 + 1)
= (12 + 1)(32 + 1)(122 + 1)(702 + 1) = (22 + 1)(172 + 1)(992 + 1)
= (22 + 1)(52 + 1)(82 + 1)(412 + 1) = (32 + 1)(122 + 1)(992 + 1)
= (32 + 1)(172 + 1)(702 + 1) = (52 + 1)(182 + 1)(412 + 1) = (52 + 4)(242 + 4)(292 + 4).
37702 = 382 + 392 + 402 + 412 + 422 + 432 + ... + 3492.
Loop of length 5 (See 41):
3770 -- 372 + 702 = 6269 -- 622 + 692 = 8605 -- 862 + 052 = 7421 -- 742 + 212 = 5917 - 592 + 172 = 3770
by Yoshio Mimura, Kobe, Japan
3772
37724 = 202435528704256, and 22 + 02 + 242 + 352 + 52 + 22 + 82 + 72 + 02 + 422 + 52 + 62 = 3772.
Page of Squares : First Upload December 1, 2008 ; Last Revised December 1, 2008by Yoshio Mimura, Kobe, Japan
3773
37732 = (123 + 124 + 125 + 126 + 127 + 128 + 129)2 + (130 + 131 + 132 + 133 + 134 + 135 + 136)2 + (137 + 138 + 139 + 140 + 141 + 142 + 143)2 + ... + (193 + 194 + 195 + 196 + 197 + 198 + 199)2.
Page of Squares : First Upload July 17, 2007 ; Last Revised July 17, 2007by Yoshio Mimura, Kobe, Japan
3775
37752 = 14250625, a zigzag square.
Page of Squares : First Upload July 17, 2007 ; Last Revised July 17, 2007by Yoshio Mimura, Kobe, Japan
3776
37762 = 323 + 1443 + 2243.
37762 = 14258176, 12 + 42 + 22 + 52 + 82 + 12 + 72 + 62 = 142.
Page of Squares : First Upload July 17, 2007 ; Last Revised August 18, 2008by Yoshio Mimura, Kobe, Japan
3777
37772 = 14265729, a zigzag square.
37772 = 74 + 464 + 464 + 484.
Page of Squares : First Upload July 17, 2007 ; Last Revised August 18, 2008by Yoshio Mimura, Kobe, Japan
3779
37792 = 643 + 1383 + 2253.
Page of Squares : First Upload August 18, 2008 ; Last Revised August 18, 2008by Yoshio Mimura, Kobe, Japan
3780
37802 = (12 + 5)(22 + 5)(32 + 5)(52 + 5)(252 + 5) = (12 + 5)(32 + 5)(52 + 5)(72 + 5)(102 + 5)
= (12 + 5)(52 + 5)(112 + 5)(252 + 5) = (22 - 1)(42 - 1)(82 - 1)(712 - 1) = (22 - 1)(92 - 1)(2442 - 1)
= (32 + 5)(52 + 5)(72 + 5)(252 + 5).
Komachi equations:
37802 = 122 * 32 / 42 * 52 / 62 * 72 * 82 * 92 = 122 / 32 * 42 * 52 * 62 * 72 / 82 * 92.
by Yoshio Mimura, Kobe, Japan
3783
37832 = 24 + 224 + 514 + 524 = 134 + 344 + 424 + 564.
The square root of 3783 is 61.506..., and 61 = 52 + 02 + 62.
Page of Squares : First Upload July 17, 2007 ; Last Revised August 18, 2008by Yoshio Mimura, Kobe, Japan
3784
37842 = 14318656, 1 * 431 * 8 + 6 * 56 = 3784.
Page of Squares : First Upload July 17, 2007 ; Last Revised July 17, 2007by Yoshio Mimura, Kobe, Japan
3786
37862 = 1023 + 1673 + 2053.
Page of Squares : First Upload August 18, 2008 ; Last Revised August 18, 2008by Yoshio Mimura, Kobe, Japan
3787
37872 = 14341369, 12 + 42 + 32 + 42 + 12 + 32 + 62 + 92 = 132.
Page of Squares : First Upload July 17, 2007 ; Last Revised July 17, 2007by Yoshio Mimura, Kobe, Japan
3788
37882 = 30 + 32 + 33 + 315.
Page of Squares : First Upload August 30, 2011 ; Last Revised August 30, 2011by Yoshio Mimura, Kobe, Japan
3789
37892 = 613 + 1713 + 2093.
Page of Squares : First Upload August 18, 2008 ; Last Revised August 18, 2008by Yoshio Mimura, Kobe, Japan
3790
The square root of 3790 is 61.56..., and 61 = 52 + 62.
Page of Squares : First Upload July 17, 2007 ; Last Revised July 17, 2007by Yoshio Mimura, Kobe, Japan
3792
37922 = 14379264.
37922 = 14379264, 1 - 4 + 3 + 79 * 2 * 6 * 4 = 3792.
Page of Squares : First Upload July 17, 2007 ; Last Revised July 17, 2007by Yoshio Mimura, Kobe, Japan
3793
37932 = 14386849, a zigzag square.
A cubic polynomial :
(X + 18042)(X + 21122)(X + 25832) = X3 + 37932X2 + 81234122X + 98413539842.
1 / 3793 = 0.000263643553915, 262 + 362 + 42 + 32 + 52 + 52 + 392 + 152 = 3793.
Page of Squares : First Upload July 17, 2007 ; Last Revised July 17, 2007by Yoshio Mimura, Kobe, Japan
3795
37952 = 663 + 1373 + 2263 = 1323 + 1703 + 1933.
37952 = 14402025, 144 = 122 and 2025 = 452.
37952 = 5122 + 5132 + 5142 + 5152 + 5162 + 5172 + ... + 5612.
37952 = (63 + 9)(403 + 9).
Page of Squares : First Upload July 17, 2007 ; Last Revised December 21, 2013by Yoshio Mimura, Kobe, Japan
3796
Loop of length 56 by the function f(N) = ... + c2 + b2 + a2 where N = ... + 1002c + 100b + a:
3796 - 10585 - 7251 - 7785 - ... - 2570 - 5525 - 3650 - 3796
(Note f(3796) = 372 + 962 = 10585, f(10585) = 12 + 052 + 852 = 7251, etc. See 41)
by Yoshio Mimura, Kobe, Japan