5700
57002 = 403 + 2223 + 2783 = 1183 + 2093 + 2793.
57002 = 32490000, and 324 = 182 and 90000 = 3002.
228k + 4104k + 5700k + 7657k are squares for k = 1,2,3 (1332, 103932, 8386032).
Page of Squares : First Upload December 25, 2007 ; Last Revised June 21, 2011by Yoshio Mimura, Kobe, Japan
5705
57052 = 473 + 2473 + 2593.
Page of Squares : First Upload September 22, 2008 ; Last Revised September 22, 2008by Yoshio Mimura, Kobe, Japan
5708
1 / 5708 = 0.00017519, 12 + 752 + 12 + 92 = 5708.
Page of Squares : First Upload December 25, 2007 ; Last Revised December 25, 2007by Yoshio Mimura, Kobe, Japan
5709
1122k + 1353k + 2508k + 4818k are squares for k = 1,2,3 (992, 57092, 3626372).
Page of Squares : First Upload June 21, 2011 ; Last Revised June 21, 2011by Yoshio Mimura, Kobe, Japan
5711
The square root of 5711 is 75.571..., and 75 = 52 + 72 + 12.
5711 is the first prime for which the Legendre symbol (a / 5711) = 1 for a = 1, 2,..., 18.
(5711 is the 3rd prime for which the Legendre symbol (a / 5711) = 1 for a = 1, 2,..., 16).
by Yoshio Mimura, Kobe, Japan
5712
57122 = 1283 + 2443 + 2523.
Page of Squares : First Upload September 22, 2008 ; Last Revised September 22, 2008by Yoshio Mimura, Kobe, Japan
5713
Loop of length 10 by the function f(N) = ... + c2 + b2 + a2 where N = ... + 1002c + 100b + a:
5713 - 3418 - 1480 - 6596 - ... - 1268 - 4768 - 6833 - 5713
(Note f(5713) = 572 + 132 = 3418, f(3418) = 342 + 182 = 1480, etc. See 1268)
by Yoshio Mimura, Kobe, Japan
5714
57142 = 32649796, a zigzag square.
Page of Squares : First Upload December 25, 2007 ; Last Revised December 25, 2007by Yoshio Mimura, Kobe, Japan
5719
S2(5719) = S2(4) x S2(21) x S2(123).
Page of Squares : First Upload December 25, 2007 ; Last Revised December 25, 2007by Yoshio Mimura, Kobe, Japan
5720
57202 = 185 x 186 + 186 x 187 + 187 x 188 + 188 x 189 + ... + 470 x 471.
Page of Squares : First Upload December 25, 2007 ; Last Revised December 25, 2007by Yoshio Mimura, Kobe, Japan
5723
57232 = 32752729, 32 + 22 + 72 + 52 + 22 + 72 + 22 + 92 = 152.
57232 = 32752729, 3275 + 272 * 9 = 5723.
Page of Squares : First Upload December 25, 2007 ; Last Revised December 25, 2007by Yoshio Mimura, Kobe, Japan
5727
57272 = 1093 + 2373 + 2633.
Page of Squares : First Upload September 22, 2008 ; Last Revised September 22, 2008by Yoshio Mimura, Kobe, Japan
5728
57282 = 32809984, 32 * 80 + 99 * 8 * 4 = 5728.
Page of Squares : First Upload December 25, 2007 ; Last Revised December 25, 2007by Yoshio Mimura, Kobe, Japan
5732
57322 = 663 + 1303 + 3123.
Page of Squares : First Upload September 22, 2008 ; Last Revised September 22, 2008by Yoshio Mimura, Kobe, Japan
5733
57335 = 6193123048039183893 : 612 + 92 + 32 + 122 + 32 + 02 + 42 + 82 + 02 + 32 + 92 + 12 + 82 + 382 + 92 + 32 = 5733.
Page of Squares : First Upload December 8, 2008 ; Last Revised December 8, 2008by Yoshio Mimura, Kobe, Japan
5734
57342 = 13 + 1583 + 3073.
Page of Squares : First Upload September 22, 2008 ; Last Revised September 22, 2008by Yoshio Mimura, Kobe, Japan
5735
57355 = 6203933174657834375 : 62 + 22 + 02 + 32 + 92 + 32 + 32 + 12 + 72 + 462 + 572 + 82 + 32 + 42 + 32 + 72 + 52 = 5735.
Page of Squares : First Upload December 8, 2008 ; Last Revised December 8, 2008by Yoshio Mimura, Kobe, Japan
5737
57375 = 6214758391312632457 : 62 + 22 + 12 + 472 + 52 + 82 + 32 + 92 + 132 + 12 + 22 + 62 + 322 + 452 + 72 = 62 + 212 + 42 + 72 + 582 + 32 + 92 + 12 + 312 + 262 + 32 + 22 + 42 + 52 + 72 = 5737.
Page of Squares : First Upload December 8, 2008 ; Last Revised December 8, 2008by Yoshio Mimura, Kobe, Japan
5739
57392 = 13 + 923 + 3183.
57392 = 32936121, a zigzag square.
1 / 5739 = 0.00017424, and 17424 = 1322.
Page of Squares : First Upload December 25, 2007 ; Last Revised September 22, 2008by Yoshio Mimura, Kobe, Japan
5740
Komachi equations:
57402 = 1232 / 42 * 52 * 62 * 72 * 82 / 92 = 1232 * 452 / 62 * 72 * 82 / 92.
by Yoshio Mimura, Kobe, Japan
5741
57412 = 673 + 1553 + 3073.
57412 = 32959081, a zigzag square.
57412 = 40592 + 40602.
Page of Squares : First Upload December 25, 2007 ; Last Revised September 22, 2008by Yoshio Mimura, Kobe, Japan
5742
57422 = 32970564, a square with different digits.
3553k + 4554k + 5742k + 6600k are squares for k = 1,2,3 (1432, 104832, 7849272).
Page of Squares : First Upload December 25, 2007 ; Last Revised June 21, 2011by Yoshio Mimura, Kobe, Japan
5751
57512 = 1263 + 2253 + 2703.
Page of Squares : First Upload September 22, 2008 ; Last Revised September 22, 2008by Yoshio Mimura, Kobe, Japan
5752
57525 = 6296430107020460032 : 62 + 22 + 92 + 642 + 32 + 02 + 12 + 02 + 72 + 02 + 202 + 42 + 62 + 02 + 02 + 322 = 5752.
Page of Squares : First Upload December 8, 2008 ; Last Revised December 8, 2008by Yoshio Mimura, Kobe, Japan
5754
57542± 5 are primes.
57542 = 2053 + 2303 + 2313.
Page of Squares : First Upload September 22, 2008 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
5756
57562 = 33131536, 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
5760
57602 = (22 - 1)(32 - 1)(42 - 1)(52 - 1)(72 - 1)(92 - 1) = (22 - 1)(32 - 1)(72 - 1)(92 - 1)(192 - 1)
= (22 - 1)(52 - 1)(72 - 1)(92 - 1)(112 - 1) = (32 - 1)(42 - 1)(172 - 1)(312 - 1)
= (52 - 1)(72 - 1)(92 - 1)(192 - 1) = (72 - 1)(172 - 1)(492 - 1) = (112 - 1)(172 - 1)(312 - 1).
57602 = 1283 + 1443 + 3043 = 1963 + 2103 + 2543.
57602 = (55 + 56 + 57 + ... + 69)2 + (70 + 71 + 72 + ... + 84)2 + (85 + 86 + 87 + ... + 99)2 + ... + (175 + 176 + 177 + ... + 189)2.
Page of Squares : First Upload December 25, 2007 ; Last Revised December 28, 2013by Yoshio Mimura, Kobe, Japan
5762
57622 = 174 + 414 + 474 + 714.
Page of Squares : First Upload September 22, 2008 ; Last Revised September 22, 2008by Yoshio Mimura, Kobe, Japan
5765
57652 = 33235225, a square consisting of just 3 kinds of digita.
57652 = 33235225, 3 * 32 * 3 * 5 * 2 * 2 + 5 = 5765.
Page of Squares : First Upload December 25, 2007 ; Last Revised December 25, 2007by Yoshio Mimura, Kobe, Japan
5766
S2(5766) = S22(3921) + S2(5084), where S2(n) = 12 + 22 + 32 + ... + n2.
57662 = 33246756, 3 * 3 * 2 * 46 * 7 - 5 * 6 = 5766.
Page of Squares : First Upload December 25, 2007 ; Last Revised December 25, 2007by Yoshio Mimura, Kobe, Japan
5767
57672 = 33258289, 3 * 3 - 2 + 5 * 8 * 2 * 8 * 9 = 5767.
Page of Squares : First Upload December 25, 2007 ; Last Revised December 25, 2007by Yoshio Mimura, Kobe, Japan
5768
57682 = 1943 + 2323 + 2383.
1 / 5768 = 0.0001733703190013, 12 + 732 + 32 + 72 + 032 + 192 + 0012 + 32 = 5768.
Page of Squares : First Upload December 25, 2007 ; Last Revised September 22, 2008by Yoshio Mimura, Kobe, Japan
5769
57692 = 124 + 304 + 304 + 754.
Page of Squares : First Upload September 22, 2008 ; Last Revised September 22, 2008by Yoshio Mimura, Kobe, Japan
5775
57752± 2 are primes.
57752 = (12 + 6)(32 + 6)(152 + 6)(372 + 6) = (272 + 6)(2132 + 6)
= (32 + 6)(72 + 6)(132 + 6)(152 + 6).
57752 = 203 + 2253 + 2803.
Page of Squares : First Upload September 22, 2008 ; Last Revised December 29, 2013by Yoshio Mimura, Kobe, Japan
5776
The square of 76.
Page of Squares : First Upload December 25, 2007 ; Last Revised December 25, 2007by Yoshio Mimura, Kobe, Japan
5777
57772 = 893 + 1663 + 3043 = 284 + 544 + 544 + 634.
5777 and 5993 are counter examples for the statement that every odd integer is the sum of a power of 2 and a prime (the third counter example is greater than 6*105 if it exists).
Page of Squares : First Upload December 25, 2007 ; Last Revised September 22, 2008by Yoshio Mimura, Kobe, Japan
5778
57782 = (22 + 2)(312 + 2)(762 + 2).
Page of Squares : First Upload December 28, 2013 ; Last Revised December 28, 2013by Yoshio Mimura, Kobe, Japan
5779
57792 = 33396841, 32 + 32 + 32 + 92 + 62 + 82 + 42 + 12 = 152.
Page of Squares : First Upload December 25, 2007 ; Last Revised December 25, 2007by Yoshio Mimura, Kobe, Japan
5780
57802 = (82 + 4)(92 + 4)(762 + 4).
Page of Squares : First Upload December 28, 2013 ; Last Revised December 28, 2013by Yoshio Mimura, Kobe, Japan
5781
57812 = 23 + 1453 + 3123.
57814 = 1116893793241521,
and 12 + 112 + 682 + 92 + 32 + 72 + 92 + 32 + 242 + 152 + 22 + 12 = 5781,
57814 = 1116893793241521,
and 112 + 12 + 682 + 92 + 32 + 72 + 92 + 32 + 242 + 152 + 22 + 12 = 5781.
by Yoshio Mimura, Kobe, Japan
5782
57822± 3 are primes.
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
5783
57832 = 543 + 1703 + 3053.
Page of Squares : First Upload September 22, 2008 ; Last Revised September 22, 2008by Yoshio Mimura, Kobe, Japan
5785
57852 = (292 + 4)(1992 + 4).
Loop of length 35 by the function f(N) = ... + c2 + b2 + a2 where N = ... + 1002c + 100b + a:
5785 - 10474 - 5493 - 11565 - ... - 7034 - 6056 - 6736 - 5785
(Note f(5785) = 572 + 852 = 10474, f(10474) = 12 + 042 + 742 = 5493, etc. See 37)
57852 = 33466225 appears in the decimal expressions of e:
e = 2.71828•••33466225••• (from the 20869th digit)
(33466225 is the second 8-digit square in the expression of e.)
by Yoshio Mimura, Kobe, Japan
5790
57902 = 1093 + 1643 + 3033.
Page of Squares : First Upload September 22, 2008 ; Last Revised September 22, 2008by Yoshio Mimura, Kobe, Japan
5795
5795 = (12 + 22 + 32 + ... + 1522) / (12 + 22 + 32 + ... + 82).
57952 = 33582025, 3 - 3 + 5820 - 25 = 3 / 3 * 5820 - 25 = 5795.
Page of Squares : First Upload December 25, 2007 ; Last Revised November 25, 2008by Yoshio Mimura, Kobe, Japan
5796
5796 = (12 + 22 + 32 + ... + 802) / (12 + 22 + 32 + 42).
57962 = 1303 + 1403 + 3063.
The integral triangle of sides 1820, 83441, 85077 has square area 57962.
Page of Squares : First Upload September 22, 2008 ; Last Revised October 14, 2011by Yoshio Mimura, Kobe, Japan
5797
5797 = (12 + 22 + 32 + ... + 1702) / (12 + 22 + 32 + ... + 92).
57972 = 813 + 2203 + 2823 = 1653 + 2193 + 2653.
Page of Squares : First Upload September 22, 2008 ; Last Revised November 25, 2008by Yoshio Mimura, Kobe, Japan