3600
The square of 60.
36002 = (22 - 1)(42 - 1)(112 - 1)(492 - 1) = (32 - 1)(262 - 1)(492 - 1) = (42 - 1)(192 - 1)(492 - 1).
36002 = 403 + 903 + 2303.
A cubic polynomial :
(X + 19202)(X + 27372)(X + 36002) = X3 + 49132X2 + 131330402X + 189181440002.
A 4-cycle : 36002 = 12960000 -- 96002 = 92160000 -- 16002 = 02560000 -- 56002 = 31360000
Other examples : 2916 -- 5030 -- 3009 -- 0540 -- 2916, abd 2100 -- 4100 -- 8100 -- 6100 -- 2100.
Komachi equation: 36002 = 94 * 84 * 74 * 64 * 54 / 44 / 34 / 214.
36002 = (3 + 4 + 5 + ... + 17)2 + (18 + 19 + 20 + ... + 32)2 + (33 + 34 + 35 + ... + 47)2 + ... + (123 + 124 + 125 + ... + 137)2.
Page of Squares : First Upload July 9, 2007 ; Last Revised December 21, 2013by Yoshio Mimura, Kobe, Japan
3602
36022 = 12974404, 129 * 7 * 4 - 40 / 4 = 3602.
Page of Squares : First Upload July 9, 2007 ; Last Revised July 9, 2007by Yoshio Mimura, Kobe, Japan
3603
36032 = 733 + 1733 + 1953.
Page of Squares : First Upload August 18, 2008 ; Last Revised August 18, 2008by Yoshio Mimura, Kobe, Japan
3604
36042 = (72 + 4)(82 + 4)(602 + 4).
36042 = 83 + 1383 + 2183.
Page of Squares : First Upload August 18, 2008 ; Last Revised December 21, 2013by Yoshio Mimura, Kobe, Japan
3605
36052 = 12996025, and 12996 = 1142, 25 = 52.
Page of Squares : First Upload July 9, 2007 ; Last Revised July 9, 2007by Yoshio Mimura, Kobe, Japan
3608
36082 = 6122 + 6132 + 6142 + 6152 + ... + 6442.
Page of Squares : First Upload July 9, 2007 ; Last Revised July 9, 2007by Yoshio Mimura, Kobe, Japan
3609
3609 = (12 + 22 + 32 + ... + 14032) / (12 + 22 + 32 + ... + 912).
Page of Squares : First Upload November 25, 2008 ; Last Revised November 25, 2008by Yoshio Mimura, Kobe, Japan
3610
1330k + 3610k + 5690k + 6270k are squares for k = 1,2,3 (1302, 93002, 6929002).
Page of Squares : First Upload June 7, 2011 ; Last Revised June 7, 2011by Yoshio Mimura, Kobe, Japan
3612
1 / 3612 = 0.000276854928017, 272 + 62 + 82 + 52 + 492 + 22 + 82 + 0172 = 3612.
36122 = (22 + 3)(32 + 3)(132 + 3)(302 + 3) = (92 + 3)(132 + 3)(302 + 3).
Komachi equations:
36122 = 92 * 82 * 72 / 62 * 52 * 432 * 22 / 102 = 92 * 82 * 72 / 62 / 52 * 432 / 22 * 102
= 982 / 72 * 62 * 52 * 432 * 22 / 102 = 982 / 72 * 62 / 52 * 432 / 22 * 102.
by Yoshio Mimura, Kobe, Japan
3613
36132 = 13053769, a zigzag square.
Page of Squares : First Upload July 9, 2007 ; Last Revised July 9, 2007by Yoshio Mimura, Kobe, Japan
3614
1 / 3614 = 0.000276701715550, 272 + 62 + 72 + 012 + 72 + 152 + 52 + 502 = 3614.
Page of Squares : First Upload July 9, 2007 ; Last Revised July 9, 2007by Yoshio Mimura, Kobe, Japan
3617
36172 = 13082689, 1 + 3082 + 6 * 89 = 3617.
Loop of length 56 by the function f(N) = ... + c2 + b2 + a2 where N = ... + 1002c + 100b + a:
3617 - 1585 - 7450 - 7976 - ... - 4432 - 2960 - 4441 - 3617
(Note f(3617) = 362 + 172 = 1585, f(1585) = 152 + 852 = 7450, etc. See 41)
by Yoshio Mimura, Kobe, Japan
3618
36182 = 903 + 993 + 2253 = 1343 + 1413 + 1993.
36182 = 13089924, 12 + 32 + 02 + 82 + 92 + 92 + 22 + 42 = 162.
36183 = 47359345032, and 42 + 72 + 32 + 592 + 32 + 42 + 52 + 02 + 32 + 22 = 3618.
Page of Squares : First Upload July 9, 2007 ; Last Revised December 1, 2008by Yoshio Mimura, Kobe, Japan
3619
36192 = 883 + 1613 + 2023.
36195 = 620787431434654099 : 62 + 202 + 72 + 82 + 72 + 42 + 32 + 12 + 42 + 342 + 62 + 52 + 402 + 92 + 92 = 3619.
Page of Squares : First Upload August 18, 2008 ; Last Revised December 8, 2008by Yoshio Mimura, Kobe, Japan
3621
36212± 2 are primes.
3621k + 16543k + 16685k + 43807k are squares for k = 1,2,3 (2842, 498422, 96585562).
Page of Squares : First Upload June 7, 2011 ; Last Revised December 29, 2013by Yoshio Mimura, Kobe, Japan
3622
36222± 3 are primes.
36222 = 983 + 1493 + 2073.
36225 = 623364735242561632 : 62 + 22 + 32 + 32 + 62 + 42 + 72 + 32 + 52 + 22 + 42 + 22 + 562 + 162 + 32 + 22 = 3622.
Page of Squares : First Upload August 18, 2008 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
3624
36242 = 13133376, a square with odd digits except the last digit 6.
3624, 3625, 3626, 3627 and 3628 are five consecutive integers having square factors (the 4th case).
Page of Squares : First Upload November 10, 2008 ; Last Revised December 14, 2013by Yoshio Mimura, Kobe, Japan
3625
36252 = 13140625, a zigzag square.
Page of Squares : First Upload July 9, 2007 ; Last Revised July 9, 2007by Yoshio Mimura, Kobe, Japan
3626
36262 = 883 + 1313 + 2173.
36262 = 13147876, 12 + 32 + 12 + 42 + 72 + 82 + 72 + 62 = 152.
2282k + 3010k + 3626k + 6958k are squares for k = 1,2,3 (1262, 87082, 6509162).
154k + 3038k + 3626k + 9058k are squares for k = 1,2,3 (1262, 102202, 9049322).
by Yoshio Mimura, Kobe, Japan
3632
36322 = 13191424, a zigzag square.
36322 = 83 + 363 + 2363.
Page of Squares : First Upload July 9, 2007 ; Last Revised August 18, 2008by Yoshio Mimura, Kobe, Japan
3639
36392 = 13242321, a square every digit of which is non-zero and smaller than 5.
36392 = 93 + 463 + 2363.
Page of Squares : First Upload August 18, 2008 ; Last Revised September 7, 2013by Yoshio Mimura, Kobe, Japan
3641
36415 = 639887158501154201 : 62 + 392 + 82 + 82 + 72 + 12 + 52 + 82 + 52 + 02 + 12 + 12 + 52 + 422 + 02 + 12 = 3641.
Page of Squares : First Upload December 8, 2008 ; Last Revised December 8, 2008by Yoshio Mimura, Kobe, Japan
3644
1 / 3644 = 0.00027442371020, 272 + 442 + 232 + 72 + 12 + 02 + 202 = 3644,
1 / 3644 = 0.00027442371020, 272 + 442 + 232 + 72 + 12 + 0202 = 3644.
by Yoshio Mimura, Kobe, Japan
3645
36452 = (68 + 69 + 70 + ... + 94)2 + (95 + 96 + 97 + ... + 121)2 + (122 + 123 + 124 + ... + 148)2 + ... + (95 + 96 + 97 + ... + 121)2.
Komachi equation: 36452 = 92 / 82 / 72 * 62 * 542 / 32 * 2102.
Page of Squares : First Upload July 9, 2007 ; Last Revised October 4, 2010by Yoshio Mimura, Kobe, Japan
3646
36462 = 13293316, 1 + 329 + 3316 = 3646.
Page of Squares : First Upload July 9, 2007 ; Last Revised July 9, 2007by Yoshio Mimura, Kobe, Japan
3648
36482 = 43 + 873 + 2333 = 83 + 1843 + 1923.
Page of Squares : First Upload August 18, 2008 ; Last Revised August 18, 2008by Yoshio Mimura, Kobe, Japan
3649
36492 = (19 + 20 + 21 + ... + 59)2 + (60 + 61 + 62 + ... + 100)2.
Page of Squares : First Upload July 9, 2007 ; Last Revised July 9, 2007by Yoshio Mimura, Kobe, Japan
3650
Loop of length 56 by the function f(N) = ... + c2 + b2 + a2 where N = ... + 1002c + 100b + a:
3650 - 3796 - 10585 - 7251 - ... - 4913 - 2570 - 5525 - 3650
(Note f(3650) = 362 + 502 = 3796, f(3796) = 372 + 962 = 10585, etc. See 41)
by Yoshio Mimura, Kobe, Japan
3651
36512 = 13329801, 12 + 32 + 32 + 22 + 92 + 82 + 02 + 12 = 132.
Page of Squares : First Upload July 9, 2007 ; Last Revised July 9, 2007by Yoshio Mimura, Kobe, Japan
3653
36532 = 43 + 813 + 2343.
Page of Squares : First Upload August 18, 2008 ; Last Revised August 18, 2008by Yoshio Mimura, Kobe, Japan
3654
36542 = 13351716, 13 * 3 + 51 * 71 - 6 = 3654.
36542 = 13351716, a square with odd digits except the last digit 6.
36542 = (132 + 5)(162 + 5)(172 + 5) = (132 + 5)(2772 + 5) = (22 + 5)(172 + 5)(712 + 5)
= (22 + 5)(32 + 5)(42 + 5)(712 + 5) = (32 + 5)(132 + 5)(742 + 5) = (32 + 5)(42 + 5)(132 + 5)(162 + 5)
= (42 + 5)(112 + 5)(712 + 5).
by Yoshio Mimura, Kobe, Japan
3655
36552 = 13 + 1223 + 2263.
Page of Squares : First Upload August 18, 2008 ; Last Revised August 18, 2008by Yoshio Mimura, Kobe, Japan
3656
36562 = 13366336, a square with just 3 kinds of digits.
1 / 3656 = 0.00027352297, 22 + 72 + 32 + 522 + 292 + 72 = 3656.
Page of Squares : First Upload July 9, 2007 ; Last Revised July 9, 2007by Yoshio Mimura, Kobe, Japan
3657
36572 = 13373649, 1 + 3 - 3 + 7 + 3649 = 1 + 3 / 3 * 7 + 3649 = 1 - 3 + 3 + 7 + 3649 = 3657
= 1 * 3 / 3 + 7 + 3649 = 1 / 3 * 3 + 7 + 3649 = 133 / 7 * 3 * 64 + 9 = 3657.
by Yoshio Mimura, Kobe, Japan
3663
36632 = 64 + 114 + 384 + 584.
36632 = 13417569, 134 + 1 + 7 * 56 * 9 = 3663.
Page of Squares : First Upload July 9, 2007 ; Last Revised August 18, 2008by Yoshio Mimura, Kobe, Japan
3666
Komachi equation: 36662 = 9872 * 652 * 42 * 32 / 2102.
Page of Squares : First Upload July 9, 2007 ; Last Revised October 4, 2010by Yoshio Mimura, Kobe, Japan
3667
36672 = 12446889, a square with non-decreasing digits.
36672 = 723 + 1583 + 2093.
627k + 3667k + 8037k + 10773k are squares for k = 1,2,3 (1522, 139462, 13486962).
Page of Squares : First Upload July 9, 2007 ; Last Revised June 7, 2011by Yoshio Mimura, Kobe, Japan
3669
36692 = 723 + 763 + 2333.
36694 = 181213624556721, and 182 + 12 + 22 + 132 + 62 + 22 + 42 + 552 + 62 + 72 + 22 + 12 = 3669.
Page of Squares : First Upload August 18, 2008 ; Last Revised December 1, 2008by Yoshio Mimura, Kobe, Japan
3671
3671 is the 9th prime for which the Lendre symbol (a/3671) = 1 for a = 1,2,...,12.
36712 = 13476241, 13 * 47 * 6 + 2 + 4 - 1 = 3671.
Page of Squares : First Upload July 9, 2007 ; Last Revised July 9, 2007by Yoshio Mimura, Kobe, Japan
3672
36722 = (94 + 95 + 96 + 97 + 98 + 99 + 100 + 101 + 102)2 + (103 + 104 + 105 + 106 + 107 + 108 + 109 + 110 + 111)2 + (112 + 113 + 114 + 115 + 116 + 117 + 118 + 119 + 120)2 + ... + (166 + 167 + 168 + 169 + 170 + 171 + 172 + 173 + 174)2.
36722 = (32 + 8)(202 + 8)(442 + 8) = (42 + 8)(202 + 8)(372 + 8).
Komachi equations:
36722 = 122 * 342 * 562 / 72 / 82 * 92 = 122 * 342 / 562 * 72 * 82 * 92
= 92 * 82 * 7652 * 42 / 32 / 22 / 102.
by Yoshio Mimura, Kobe, Japan
3673
1 / 3673 = 0.00027225..., and 27225 = 1652.
Page of Squares : First Upload July 9, 2007 ; Last Revised July 9, 2007by Yoshio Mimura, Kobe, Japan
3674
36742 = 13498276, a square with diffrent digits.
Page of Squares : First Upload July 9, 2007 ; Last Revised July 9, 2007by Yoshio Mimura, Kobe, Japan
3675
36752 = (12 + 6)(32 + 6)(132 + 6)(272 + 6).
Page of Squares : First Upload December 21, 2013 ; Last Revised December 21, 2013by Yoshio Mimura, Kobe, Japan
3678
36782 = 13527684, q square with different digits.
Page of Squares : First Upload July 9, 2007 ; Last Revised July 9, 2007by Yoshio Mimura, Kobe, Japan
3682
1 / 3682 = 0.000271591526344, 272 + 12 + 52 + 92 + 152 + 262 + 32 + 442 = 3682,
1 / 3682 = 0.000271591526344, 272 + 152 + 92 + 12 + 52 + 262 + 32 + 442 = 3682.
36822 = 13557124, 1 + 3557 + 124 = 13 * 5 * 57 + 1 - 24 = 3682.
Page of Squares : First Upload July 9, 2007 ; Last Revised July 9, 2007by Yoshio Mimura, Kobe, Japan
3689
3689 = (12 + 22 + 32 + ... + 24642) / (12 + 22 + 32 + ... + 1592).
Page of Squares : First Upload November 25, 2008 ; Last Revised November 25, 2008by Yoshio Mimura, Kobe, Japan
3690
36902 = (22 + 5)(52 + 5)(62 + 5)(352 + 5) = (92 + 9)(142 + 9)(272 + 9).
Page of Squares : First Upload December 21, 2013 ; Last Revised December 21, 2013, 2007by Yoshio Mimura, Kobe, Japan
3692
36922± 3 are primes.
36922 = 13630864, 1 / 3 * 6 * 308 * 6 - 4 = 3692.
Page of Squares : First Upload July 9, 2007 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
3693
36932 = 703 + 1133 + 2283.
Page of Squares : First Upload August 18, 2008 ; Last Revised August 18, 2008by Yoshio Mimura, Kobe, Japan
3696
36962 = 13660416, 1 + 3660 + 41 - 6 = 3696.
652 + 3696 = 892, 652 - 3696 = 232.
Page of Squares : First Upload July 9, 2007 ; Last Revised July 27, 2011by Yoshio Mimura, Kobe, Japan
3697
36972 = 364 + 424 + 424 + 494.
1 / 3697 = 0.0002704..., and 2704 = 522.
36973 = 50529889873, and 502 + 52 + 292 + 82 + 82 + 92 + 82 + 72 + 32 = 3697.
Page of Squares : First Upload July 9, 2007 ; Last Revised December 1, 2008by Yoshio Mimura, Kobe, Japan
3698
36982 = 434 + 434 + 434 + 434.
1 / 3698 = 0.0002704..., and 2704 = 522.
36982 = 13675204, a square with different digits.
Page of Squares : First Upload July 9, 2007 ; Last Revised August 18, 2008by Yoshio Mimura, Kobe, Japan