2700
27002 = 903 + 903 + 1803.
27002 = (12 + 9)(32 + 9)(92 + 9)(212 + 9).
Page of Squares : First Upload July 24, 2008 ; Last Revised December 21, 2013by Yoshio Mimura, Kobe, Japan
2701
27012 = 7295401, a square with different digits.
27012 = 7295401 appears in the decimal expressions of π:
π = 3.14159•••7295401••• (from the 93597th digit)
by Yoshio Mimura, Kobe, Japan
2702
27022 = 5402 + 5412 + 5422 + 5432 + 5442 + 5452 + ... + 5632.
Page of Squares : First Upload May 7, 2007 ; Last Revised May 7, 2007by Yoshio Mimura, Kobe, Japan
2703
27032 = 93 + 163 + 1943 = 1123 + 1203 + 1613.
Page of Squares : First Upload July 24, 2008 ; Last Revised July 24, 2008by Yoshio Mimura, Kobe, Japan
2704
The square of 52.
Komachi equation: 27042 = 984 / 74 * 654 * 44 * 34 / 2104.
Page of Squares : First Upload May 7, 2007 ; Last Revised September 24, 2010by Yoshio Mimura, Kobe, Japan
2706
27062 = (12 + 2)(302 + 2)(522 + 2) = (22 + 2)(32 + 2)(112 + 2)(302 + 2) = (82 + 2)(112 + 2)(302 + 2).
Page of Squares : First Upload December 21, 2013 ; Last Revised December 21, 2013by Yoshio Mimura, Kobe, Japan
2707
27072 = 95 + 155 + 175 + 185 + 205.
Page of Squares : First Upload July 24, 2008 ; Last Revised July 24, 2008by Yoshio Mimura, Kobe, Japan
2708
27082 = 963 + 1303 + 1623.
Page of Squares : First Upload July 24, 2008 ; Last Revised July 24, 2008by Yoshio Mimura, Kobe, Japan
2709
27092 = 253 + 833 + 1893.
Page of Squares : First Upload July 24, 2008 ; Last Revised July 24, 2008by Yoshio Mimura, Kobe, Japan
2711
27112 = 7349521, a square with different digits.
27114 = 54015458929441, and 52 + 402 + 12 + 52 + 42 + 52 + 82 + 92 + 292 + 42 + 42 + 12 = 2711.
Page of Squares : First Upload May 7, 2007 ; Last Revised December 1, 2008by Yoshio Mimura, Kobe, Japan
2715
27152± 2 are primes.
2715 = (12 + 22 + 32 + ... + 902) / (12 + 22 + 32 + 42 + 52 + 62).
27152 = 583 + 813 + 1883.
Page of Squares : First Upload July 24, 2008 ; Last Revised December 29, 2013by Yoshio Mimura, Kobe, Japan
2716
2716 = (12 + 22 + 32 + ... + 482) / (12 + 22 + 32).
Page of Squares : First Upload November 25, 2008 ; Last Revised November 25, 2008by Yoshio Mimura, Kobe, Japan
2717
2717 = (12 + 22 + 32 + ... + 1042) / (12 + 22 + 32 + ... + 72).
27172 = 163 + 1533 + 1563.
Page of Squares : First Upload July 24, 2008 ; Last Revised November 25, 2008by Yoshio Mimura, Kobe, Japan
2718
27182 = 553 + 1253 + 1743.
Page of Squares : First Upload July 24, 2008 ; Last Revised July 24, 2008by Yoshio Mimura, Kobe, Japan
2719
27192 = 183 + 1053 + 1843.
Page of Squares : First Upload July 24, 2008 ; Last Revised July 24, 2008by Yoshio Mimura, Kobe, Japan
2720
27202± 3 are primes.
27202 = 85 + 85 + 155 + 175 + 225.
27202 = (22 + 4)(42 + 4)(82 + 4)(262 + 4).
230k + 610k + 665k + 2720k are squares for k = 1,2,3 (652, 28752, 1437252).
Page of Squares : First Upload July 24, 2008 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
2721
27212± 2 are primes.
27213 = 20145851361, and 202 + 12 + 452 + 82 + 52 + 132 + 62 + 12 = 2721.
Page of Squares : First Upload December 1, 2008 ; Last Revised December 29, 2013by Yoshio Mimura, Kobe, Japan
2725
27252 = 652 + 662 + 672 + 682 + 692 + 702 + ... + 2822.
Page of Squares : First Upload May 7, 2007 ; Last Revised May 7, 2007by Yoshio Mimura, Kobe, Japan
2726
2726 = (12 + 22 + 32 + ... + 1882) / (12 + 22 + 32 + ... + 132).
Page of Squares : First Upload November 25, 2008 ; Last Revised November 25, 2008by Yoshio Mimura, Kobe, Japan
2727
2727 = (12 + 22 + 32 + ... + 2022) / (12 + 22 + 32 + ... + 142).
27272 = 7436529, a square with different digits.
27272 = 244 + 364 + 394 + 424.
Page of Squares : First Upload May 7, 2007 ; Last Revised November 25, 2008by Yoshio Mimura, Kobe, Japan
2728
27282 = 7441984, and 744 + 1984 = 2728.
27282 = (138 + 139 + 140 + 141)2 + (142 + 143 + 144 + 145)2 + (146 + 147 + 148 + 149)2 + ... + (198 + 199 + 200 + 201)2.
Page of Squares : First Upload May 7, 2007 ; Last Revised May 7, 2007by Yoshio Mimura, Kobe, Japan
2729
27292 = 7447441, a square with just 3 kinds of digits.
Page of Squares : First Upload May 7, 2007 ; Last Revised May 7, 2007by Yoshio Mimura, Kobe, Japan
2730
The integral triangle of sides 1928, 7735, 7913 (or 2205, 55133, 57322) has square area 27302.
1326k + 2730k + 5226k + 7618k are squares for k = 1,2,3 (1302, 97242, 7794282).
294k + 1288k + 1617k + 2730k are squares for k = 1,2,3 (772, 34372, 1635132).
by Yoshio Mimura, Kobe, Japan
2731
27312 = 7458361, a square with different digits.
Page of Squares : First Upload May 7, 2007 ; Last Revised May 7, 2007by Yoshio Mimura, Kobe, Japan
2732
27322 = 7469289, a zigzag square.
Komachi equations: 27322 = 986 / 76 - 66 - 56 - 46 + 36 - 26 */ 16.
Page of Squares : First Upload May 7, 2007 ; Last Revised September 24, 2010by Yoshio Mimura, Kobe, Japan
2734
27342 = 7474756, a zigzag square.
Page of Squares : First Upload May 7, 2007 ; Last Revised May 7, 2007by Yoshio Mimura, Kobe, Japan
2736
27362 = 43 + 1403 + 1683 = 1023 + 1383 + 1563 = 65 + 85 + 115 + 205 + 215.
The integral triangle of sides 3211, 4672, 5835 has square area 27362.
27362 = (22 + 8)(122 + 8)(642 + 8) = (22 + 8)(72 + 8)(82 + 8)(122 + 8) = (82 + 8)(122 + 8)(262 + 8).
27362 = 7485696 appears in the decimal expressions of e:
e = 2.71828•••7485696••• (from the 2267th digit)
(7485696 is the third 7-digit square in the expression of e.)
by Yoshio Mimura, Kobe, Japan
2737
2737 = (12 + 22 + 32 + ... + 342) / (12 + 22),
2737 = (12 + 22 + 32 + ... + 5522) / (12 + 22 + 32 + ... + 392).
27372 = 55 + 55 + 165 + 235.
667k + 2507k + 2553k + 2737k are squares for k = 1,2,3 (922, 45542, 2306442).
A cubic polynomial :
(X + 19202)(X + 27372)(X + 36002) = X3 + 49132X2 + 131330402X + 189181440002.
by Yoshio Mimura, Kobe, Japan
2738
27382 = 7496644, and 7 * 4 * 96 + 6 + 44 = 2738.
27382 = 374 + 374 + 374 + 374.
Page of Squares : First Upload May 7, 2007 ; Last Revised July 24, 2008by Yoshio Mimura, Kobe, Japan
2739
27392 = 1192 + 1212 + 1232 + 1252 + 1272 + 1292 + ... + 3592.
Page of Squares : First Upload May 7, 2007 ; Last Revised May 7, 2007by Yoshio Mimura, Kobe, Japan
2744
Komachi equation: 27442 = 96 * 86 * 76 * 66 / 56 / 4326 * 106.
27442 = 1263 + 1333 + 1473.
Page of Squares : First Upload July 24, 2008 ; Last Revised September 24, 2010by Yoshio Mimura, Kobe, Japan
2745
960k + 2080k + 2745k + 3240k are squares for k = 1,2,3 (952, 48252, 2541252).
Page of Squares : First Upload May 24, 2011 ; Last Revised May 24, 2011by Yoshio Mimura, Kobe, Japan
2749
A cubic polynomial :
(X + 8962)(X + 12692)(X + 22682) = X3 + 27492X2 + 37021322X + 25787704322.
by Yoshio Mimura, Kobe, Japan
2750
27502 = 183 + 1073 + 1853.
Page of Squares : First Upload July 24, 2008 ; Last Revised July 24, 2008by Yoshio Mimura, Kobe, Japan
2751
1 / 2751 = 0.000363504180298..., 362 + 352 + 042 + 12 + 82 + 022 + 92 + 82 = 2751.
Page of Squares : First Upload May 7, 2007 ; Last Revised May 7, 2007by Yoshio Mimura, Kobe, Japan
2752
27522 = 7573504, a zigzag square.
27522 = (12 + 7)(32 + 7)(62 + 7)(372 + 7) = (62 + 7)(112 + 7)(372 + 7).
Page of Squares : First Upload May 7, 2007 ; Last Revised December 21, 2013by Yoshio Mimura, Kobe, Japan
2753
The square root of 2753 is 52.46..., and 52 = 42 + 62.
27533 = 20865011777, and 22 + 02 + 82 + 62 + 502 + 12 + 12 + 72 + 72 + 72 = 2753.
Page of Squares : First Upload May 7, 2007 ; Last Revised December 1, 2008by Yoshio Mimura, Kobe, Japan
2754
27542 = 7584516, a zigzag square.
27542 = (12 + 2)(42 + 2)(52 + 2)(72 + 2)(102 + 2) = (12 + 2)(72 + 2)(102 + 2)(222 + 2)
= (22 + 2)(42 + 2)(2652 + 2) = (52 + 2)(222 + 2)(242 + 2).
578k + 2754k + 6358k + 8806k are squares for k = 1,2,3 (1362, 112202, 9802882).
Page of Squares : First Upload May 7, 2007 ; Last Revised December 21, 2013by Yoshio Mimura, Kobe, Japan
2755
2291k + 2465k + 2755k + 5945k are squares for k = 1,2,3 (1162, 73662, 5079642).
27552 = 7590025 appears in the decimal expressions of e:
e = 2.71828•••7590025••• (from the 40058th digit)
by Yoshio Mimura, Kobe, Japan
2756
27562 = 7595536, 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
2757
27572 = 1133 + 1243 + 1623.
Page of Squares : First Upload July 24, 2008 ; Last Revised July 24, 2008by Yoshio Mimura, Kobe, Japan
2758
27582 = 7606564 is a square pegged by 6.
Page of Squares : First Upload May 7, 2007 ; Last Revised May 7, 2007by Yoshio Mimura, Kobe, Japan
2760
2760 = (12 + 22 + 32 + ... + 2872) / (12 + 22 + 32 + ... + 202).
27602 = 110 x 111 x 112 + 112 x 113 x 114 + 114 x 115 x 116 + 116 x 117 x 118 + 118 x 119 x 120.
Page of Squares : First Upload May 7, 2007 ; Last Revised November 25, 2008by Yoshio Mimura, Kobe, Japan
2761
27612 = 25 + 45 + 165 + 175 + 225.
Page of Squares : First Upload July 24, 2008 ; Last Revised July 24, 2008by Yoshio Mimura, Kobe, Japan
2763
27632 = 173 + 823 + 1923.
1 / 2763 = 0.000361... and 361 = 192. the same for 2764, 2765,..., 2770.
Page of Squares : First Upload May 7, 2007 ; Last Revised July 24, 2008by Yoshio Mimura, Kobe, Japan
2764
27642 = 103 + 1493 + 1633 = 243 + 1063 + 1863 = 1143 + 1243 + 1623.
Page of Squares : First Upload July 24, 2008 ; Last Revised July 24, 2008by Yoshio Mimura, Kobe, Japan
2765
(27652 - 5) = (62 - 5)(72 - 5)(82 - 5)(102 - 5) = (32 - 5)(42 - 5)(62 - 5)(82 - 5)(102 - 5).
27652 = (132 + 6)(2092 + 6).
Page of Squares : First Upload May 7, 2007 ; Last Revised December 21, 2013by Yoshio Mimura, Kobe, Japan
2767
27672 = 7656289, and 7 * 65 * 6 + 28 + 9 = 2767.
Page of Squares : First Upload May 7, 2007 ; Last Revised May 7, 2007by Yoshio Mimura, Kobe, Japan
2768
27682± 3 are primes.
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
2771
The square root of 2771 is 52.64..., and 52 = 62 + 42.
Page of Squares : First Upload May 7, 2007 ; Last Revised May 7, 2007by Yoshio Mimura, Kobe, Japan
2772
The square root of 2772 is 52.64..., and 52 = 62 + 42.
2772 = (12 + 22 + 32 + ... + 1752) / (12 + 22 + 32 + ... + 122).
The integral triangle of sides 5569, 9153, 14560 (or 12100, 29407, 41499) has square area 27722.
Page of Squares : First Upload May 7, 2007 ; Last Revised October 11, 2011by Yoshio Mimura, Kobe, Japan
2773
12 + 22 + 32 + 42 + ... + 27732 = 7111533199, which consists of odd digits.
the third 10-digit sum (there are 4 10-digit sums in all.)
27732 = 623 + 643 + 1933.
141k + 1645k + 2773k + 4277k are squares for k = 1,2,3 (942, 53582, 3225142).
Page of Squares : First Upload May 7, 2007 ; Last Revised May 24, 2011by Yoshio Mimura, Kobe, Japan
2774
27742 = (62 + 2)(4502 + 2).
Page of Squares : First Upload May 7, 2007 ; Last Revised December 21, 2013by Yoshio Mimura, Kobe, Japan
2775
27752 + 27762 + 27772 + ... + 28122 = 28132 + 28142 + 28152 + ... + 28492.
Page of Squares : First Upload September 13, 2011 ; Last Revised September 13, 2011by Yoshio Mimura, Kobe, Japan
2778
27782 = 14 + 134 + 314 + 514.
Page of Squares : First Upload July 24, 2008 ; Last Revised July 24, 2008by Yoshio Mimura, Kobe, Japan
2780
27802± 3 are primes.
27802 = 13 + 1353 + 1743.
Page of Squares : First Upload July 24, 2008 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
2783
27832 = 114 + 224 + 444 + 444.
Page of Squares : First Upload July 24, 2008 ; Last Revised July 24, 2008by Yoshio Mimura, Kobe, Japan
2784
Komachi equations: 27842 = 92 * 872 * 62 / 542 * 322 */ 12.
Page of Squares : First Upload September 24, 2010 ; Last Revised September 24, 2010by Yoshio Mimura, Kobe, Japan
2787
27872 = 43 + 173 + 1983 = 253 + 1323 + 1763.
Page of Squares : First Upload July 24, 2008 ; Last Revised July 24, 2008by Yoshio Mimura, Kobe, Japan
2788
27882 = 44 + 84 + 264 + 524.
Page of Squares : First Upload July 24, 2008 ; Last Revised July 24, 2008by Yoshio Mimura, Kobe, Japan
2790
2790k + 4278k + 20274k + 34162k are squares for k = 1,2,3 (2482, 400522, 69499522).
Page of Squares : First Upload May 24, 2011 ; Last Revised May 24, 2011by Yoshio Mimura, Kobe, Japan
2793
2793k + 4578k + 13062k + 15288k are squares for k = 1,2,3 (1892, 208112, 24329972).
Page of Squares : First Upload May 24, 2011 ; Last Revised May 24, 2011by Yoshio Mimura, Kobe, Japan
2794
27942± 3 are primes.
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
2795
Komachi equations:
27952 = 92 + 82 - 72 + 652 * 432 + 22 - 102 = - 92 - 82 + 72 + 652 * 432 - 22 + 102.
by Yoshio Mimura, Kobe, Japan
2797
Loop of length 35 by the function f(N) = ... + c2 + b2 + a2 where N = ... + 1002c + 100b + a:
2797 - 10138 - 1446 - 2312 - ... - 5065 - 6725 - 5114 - 2797
(Note f(2797) = 272 + 972 = 10138, f(10138) = 12 + 012 + 382 = 1446, etc. See 37)
by Yoshio Mimura, Kobe, Japan