31001
310012 = 961062001, 961 = 312 and 62001 = 2492.
Page of Squares : First Upload May 19, 2012 ; Last Revised May 19, 2012by Yoshio Mimura, Kobe, Japan
31011
310112 = 961682121 is a reversible square (121286169 = 110132).
Page of Squares : First Upload May 19, 2012 ; Last Revised May 19, 2012by Yoshio Mimura, Kobe, Japan
31014
310142 = 9873 + 653 + 433 + 213,
310142 = 213 + 433 + 653 + 9873.
by Yoshio Mimura, Kobe, Japan
31032
310322± 5 are primes.
Page of Squares : First Upload February 19, 2014 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
31060
310602± 3 are primes.
Page of Squares : First Upload February 19, 2014 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
31080
310802 = (42 - 1)(362 - 1)(2232 - 1).
Page of Squares : First Upload February 19, 2014 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
31086
310862 = 966339396 is a square with 3 kinds of digits.
Page of Squares : First Upload May 19, 2012 ; Last Revised May 19, 2012by Yoshio Mimura, Kobe, Japan
31098
310982 = 10112 + 10122 + 10132 + ... + 15782.
Page of Squares : First Upload May 19, 2012 ; Last Revised May 19, 2012by Yoshio Mimura, Kobe, Japan
31101
311012 = 967272201 is a reversible square (102272769 = 101132).
Page of Squares : First Upload May 19, 2012 ; Last Revised May 19, 2012by Yoshio Mimura, Kobe, Japan
31104
1802 + 31104 = 2522, 1802 - 31104 = 362.
Page of Squares : First Upload May 19, 2012 ; Last Revised May 19, 2012by Yoshio Mimura, Kobe, Japan
31111
311112 = 967894321 is a reversible square (23498769 = 111132).
Page of Squares : First Upload May 19, 2012 ; Last Revised May 19, 2012by Yoshio Mimura, Kobe, Japan
31152
311522 = (42 + 8)(62 + 8)(132 + 8)(722 + 8)
311522 = 178*179*180 + 180*181*182 + 182*183*184 + 184*185*186 + ... + 304*305*306.
Page of Squares : First Upload October 26, 2103 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
31158
311582 = (12 + 2)(222 + 2)(8162 + 2) = (12 + 2)(42 + 2)(52 + 2)(8162 + 2).
Page of Squares : First Upload February 19, 2014 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
31160
311602± 3 are primes.
Page of Squares : First Upload February 19, 2014 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
31166
311662 = 971319556, a square with odd digits except the last digit 6.
Page of Squares : First Upload August 31, 2013 ; Last Revised August 31, 2013by Yoshio Mimura, Kobe, Japan
31194
311942± 5 are primes.
Page of Squares : First Upload February 19, 2014 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
31200
312002= (22 - 1)(32 - 1)(92 - 1)(142 - 1)(512 - 1) = (252 - 1)(12492 - 1)
= (52 - 1)(92 - 1)(142 - 1)(512 - 1).
312002= 809 x 810 + 810 x 811 + 811 x 812 + ... + 1510 x 1511.
Page of Squares : First Upload May 19, 2012 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
31210
312102± 3 are primes.
Page of Squares : First Upload February 19, 2014 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
31212
312122 = (12 + 2)(22 + 2)(42 + 2)(72 + 2)(102 + 2)(242 + 2) = (32 + 8)(142 + 8)(5302 + 8).
Page of Squares : First Upload February 19, 2014 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
31218
312182 = (162 + 2)(192 + 2)(1022 + 2) = (32 + 2)(162 + 2)(5862 + 2).
Page of Squares : First Upload February 19, 2014 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
31233
312332± 2 are primes.
Page of Squares : First Upload February 19, 2014 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
31248
312482 = 2173 + 2183 + 2193+ 2203 + ... + 2793.
312482 = 488*489*490 + 490*491*492 + 492*493*494 + 494*495*496 + ... + 502*503*504.
Page of Squares : First Upload May 19, 2012 ; Last Revised October 26, 2103by Yoshio Mimura, Kobe, Japan
31250
312502 = 976562500, 9 = 32 and 76562500 = 87502.
Page of Squares : First Upload May 19, 2012 ; Last Revised May 19, 2012by Yoshio Mimura, Kobe, Japan
31252
(312522-2) = (32 - 2)(52 - 2)(112 - 2)(122 - 2)(192 - 2).
Page of Squares : First Upload May 19, 2012 ; Last Revised May 19, 2012by Yoshio Mimura, Kobe, Japan
31262
312622 = (12 + 6)(42 + 6)(202 + 6)(1252 + 6).
Page of Squares : First Upload February 19, 2014 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
31290
312902 = (22 + 6)(212 + 6)(4682 + 6).
Page of Squares : First Upload February 19, 2014 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
31304
313042 = (72 + 3)(132 + 3)(3312 + 3).
Page of Squares : First Upload February 19, 2014 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
31320
313202 = (192 - 1)(282 - 1)(592 - 1) = (22 - 1)(112 - 1)(282 - 1)(592 - 1)
= (22 - 1)(32 - 1)(42 - 1)(282 - 1)(592 - 1) = (42 - 1)(282 - 1)(2892 - 1)
= (42 - 1)(52 - 1)(282 - 1)(592 - 1).
by Yoshio Mimura, Kobe, Japan
31326
313262± 5 are primes.
Page of Squares : First Upload February 19, 2014 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
31329
31329 = 1772 is a zigzag square.
Page of Squares : First Upload May 19, 2012 ; Last Revised May 19, 2012by Yoshio Mimura, Kobe, Japan
31367
313672 = 983888689 is a square pegged by 8.
Page of Squares : First Upload May 19, 2012 ; Last Revised May 19, 2012by Yoshio Mimura, Kobe, Japan
31370
313702± 3 are primes.
Page of Squares : First Upload February 19, 2014 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
31374
313742 = (12 + 5)(32 + 5)(242 + 5)(1422 + 5) = (22 + 5)(72 + 5)(242 + 5)(592 + 5)
= (32 + 5)(592 + 5)(1422 + 5).
by Yoshio Mimura, Kobe, Japan
31382
313822 = 1052 + 1072 + 1092 + 1112 + ... + 18072.
Page of Squares : First Upload May 19, 2012 ; Last Revised May 19, 2012by Yoshio Mimura, Kobe, Japan
31391
31391 is the first prime for which Legendre Symbol (n/31391) = 1 for n = 1,2,...,30.
Page of Squares : First Upload May 19, 2012 ; Last Revised May 19, 2012by Yoshio Mimura, Kobe, Japan
31416
314162 = (82 - 1)(332 - 1)(1202 - 1).
2052 + 31416 = 2712, 2052 - 31416 = 1032.
Page of Squares : First Upload May 19, 2012 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
31450
314502 = (12 + 1)(22 + 1)(62 + 1)(382 + 1)(432 + 1)
= (12 + 1)(42 + 1)(62 + 1)(132 + 1)(682 + 1) = (12 + 1)(682 + 1)(3272 + 1)
= (22 + 1)(32 + 1)(382 + 1)(1172 + 1) = (22 + 1)(42 + 1)(62 + 1)(132 + 1)(432 + 1)
= (22 + 1)(432 + 1)(3272 + 1) = (22 + 1)(62 + 1)(72 + 1)(3272 + 1)
= (32 + 1)(62 + 1)(382 + 1)(432 + 1) = (72 + 1)(382 + 1)(1172 + 1)
= (92 + 4)(112 + 4)(122 + 4)(252 + 4) = (92 + 4)(252 + 4)(1362 + 4)
= (192 + 9)(292 + 9)(562 + 9) = (42 + 9)(52 + 9)(192 + 9)(562 + 9).
by Yoshio Mimura, Kobe, Japan
31462
314622± 3 are primes.
Page of Squares : First Upload February 19, 2014 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
31488
314882 = 991494144 is a square with 3 kinds of digits 1, 4, 9.
Page of Squares : First Upload May 19, 2012 ; Last Revised May 19, 2012by Yoshio Mimura, Kobe, Japan
31500
315002= 710 x 711 + 711 x 712 + 712 x 713 + ... + 1493 x 1494.
Page of Squares : First Upload May 19, 2012 ; Last Revised May 19, 2012by Yoshio Mimura, Kobe, Japan
31556
315562± 3 are primes.
Page of Squares : First Upload February 19, 2014 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
31563
315632 = 996222969 is a square with 3 kinds of digits 1, 4, 9.
Page of Squares : First Upload May 19, 2012 ; Last Revised May 19, 2012by Yoshio Mimura, Kobe, Japan
31584
315842± 5 are primes.
315842 = (72 - 1)(482 - 1)(952 - 1).
Page of Squares : First Upload February 19, 2014 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
31614
316142 = 999444996 is a square with 3 kinds of digits 4, 6, 9.
Page of Squares : First Upload May 19, 2012 ; Last Revised May 19, 2012by Yoshio Mimura, Kobe, Japan
31621
316212 = 999887641 is a square the digits is non-increasing.
Page of Squares : First Upload May 19, 2012 ; Last Revised May 19, 2012by Yoshio Mimura, Kobe, Japan
31625
316252 = 1<\font color="blue">000140625, 1 = 12 and 140625 = 3752.
Page of Squares : First Upload May 19, 2012 ; Last Revised May 19, 2012by Yoshio Mimura, Kobe, Japan
31634
316342± 3 are primes.
Page of Squares : First Upload February 19, 2014 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
31648
316482= (42 + 7)(62 + 7)(272 + 7)(372 + 7).
316482= 1103 x 1104 + 1104 x 1105 + 1105 x 1106 + ... + 1631 x 1632.
Page of Squares : First Upload May 19, 2012 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
31641
The quadratic polynomial 31641X2 - 206262X + 395521 takes the values 4702, 3312, 2482, 2772, 3942, 5452 at X = 1, 2,..., 6,
Page of Squares : First Upload May 19, 2012 ; Last Revised May 19, 2012by Yoshio Mimura, Kobe, Japan
31656
The quadratic polynomial 31656X2 - 164136X + 442729 takes the values 5572, 4912, 4852, 5412, 6432, 7732 at X = 1, 2,..., 6,
Page of Squares : First Upload May 19, 2012 ; Last Revised May 19, 2012by Yoshio Mimura, Kobe, Japan
31680
316802 = (22 - 1)(32 - 1)(42 - 1)(72 - 1)(2412 - 1) = (22 - 1)(32 - 1)(102 - 1)(212 - 1)(312 - 1)
= (22 - 1)(72 - 1)(112 - 1)(2412 - 1) = (22 - 1)(92 - 1)(232 - 1)(892 - 1)
= (32 - 1)(102 - 1)(232 - 1)(492 - 1) = (32 - 1)(52 - 1)(102 - 1)(112 - 1)(212 - 1)
= (32 - 1)(52 - 1)(212 - 1)(1092 - 1) = (42 - 1)(52 - 1)(72 - 1)(2412 - 1)
= (42 - 1)(172 - 1)(212 - 1)(232 - 1) = (52 - 1)(102 - 1)(212 - 1)(312 - 1)
= (72 - 1)(192 - 1)(2412 - 1) = (72 - 1)(232 - 1)(1992 - 1) = (92 - 1)(102 - 1)(172 - 1)(212 - 1)
= (102 - 1)(492 - 1)(652 - 1) = (172 - 1)(212 - 1)(892 - 1).
by Yoshio Mimura, Kobe, Japan
31684
31684 = 1782 is a square with different digits.
Page of Squares : First Upload May 19, 2012 ; Last Revised May 19, 2012by Yoshio Mimura, Kobe, Japan
31706
317062 = 18842 + 18852 + 18862 + ... + 21322.
Page of Squares : First Upload May 19, 2012 ; Last Revised May 19, 2012by Yoshio Mimura, Kobe, Japan
31710
317102 = (32 + 6)(302 + 6)(2722 + 6).
Page of Squares : First Upload February 19, 2014 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
31716
317162± 5 are primes.
Page of Squares : First Upload February 19, 2014 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
31720
317202 = (32 + 4)(102 + 4)(222 + 4)(392 + 4).
Page of Squares : First Upload February 19, 2014 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
31744
317442± 3 are primes.
Page of Squares : First Upload February 19, 2014 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
31808
318082 = (12 + 7)(82 + 7)(212 + 7)(632 + 7).
Page of Squares : First Upload February 19, 2014 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
31817
(318172 + 3) = (22 + 3)(72 + 3)(82 + 3)(102 + 3)(202 + 3).
Page of Squares : First Upload May 19, 2012 ; Last Revised May 19, 2012by Yoshio Mimura, Kobe, Japan
31822
318222± 3 are primes.
Page of Squares : First Upload February 19, 2014 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
31824
1852 + 31824 = 2572, 1852 - 31824 = 492.
Page of Squares : First Upload May 19, 2012 ; Last Revised May 19, 2012by Yoshio Mimura, Kobe, Japan
31842
318422 = (12 + 5)(22 + 5)(422 + 5)(1032 + 5) = (12 + 5)(162 + 5)(192 + 5)(422 + 5)
= (22 + 5)(132 + 5)(192 + 5)(422 + 5) = (72 + 5)(422 + 5)(1032 + 5) = (162 + 5)(192 + 5)(1032 + 5).
by Yoshio Mimura, Kobe, Japan
31864
318642± 3 are primes.
Page of Squares : First Upload February 19, 2014 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
31874
318742± 3 are primes.
Page of Squares : First Upload February 19, 2014 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
31912
319122± 3 are primes.
Page of Squares : First Upload February 19, 2014 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
31920
4012 + 31920 = 4392, 4012 - 31920 = 3592,
1932 + 31920 = 2632, 1932 - 31920 = 732.
319202 = (202 - 1)(392 - 1)(412 - 1) = (62 - 1)(72 - 1)(202 - 1)(392 - 1).
Page of Squares : First Upload May 19, 2012 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
31935
319352± 2 are primes.
Page of Squares : First Upload February 19, 2014 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
31966
319662 = 1021825156, and 1156 = 342, 081 = 92, 225 = 152.
Page of Squares : First Upload May 19, 2012 ; Last Revised May 19, 2012by Yoshio Mimura, Kobe, Japan
31977
319772 = (12 + 2)(72 + 2)(412 + 2)(632 + 2) = (12 + 8)(32 + 8)(312 + 8)(832 + 8).
Page of Squares : First Upload February 19, 2014 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan