logo
2700 - 2799

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, 2013
by 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)

Page of Squares : First Upload May 7, 2007 ; Last Revised November 4, 2008
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, 2007
by Yoshio Mimura, Kobe, Japan

2703

27032 = 93 + 163 + 1943 = 1123 + 1203 + 1613.

Page of Squares : First Upload July 24, 2008 ; Last Revised July 24, 2008
by 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, 2010
by 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, 2013
by Yoshio Mimura, Kobe, Japan

2707

27072 = 95 + 155 + 175 + 185 + 205.

Page of Squares : First Upload July 24, 2008 ; Last Revised July 24, 2008
by Yoshio Mimura, Kobe, Japan

2708

27082 = 963 + 1303 + 1623.

Page of Squares : First Upload July 24, 2008 ; Last Revised July 24, 2008
by Yoshio Mimura, Kobe, Japan

2709

27092 = 253 + 833 + 1893.

Page of Squares : First Upload July 24, 2008 ; Last Revised July 24, 2008
by 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, 2008
by 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, 2013
by 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, 2008
by 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, 2008
by Yoshio Mimura, Kobe, Japan

2718

27182 = 553 + 1253 + 1743.

Page of Squares : First Upload July 24, 2008 ; Last Revised July 24, 2008
by Yoshio Mimura, Kobe, Japan

2719

27192 = 183 + 1053 + 1843.

Page of Squares : First Upload July 24, 2008 ; Last Revised July 24, 2008
by 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, 2014
by 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, 2013
by 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, 2007
by 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, 2008
by 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, 2008
by 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, 2007
by 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, 2007
by 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).

Page of Squares : First Upload May 24, 2011 ; Last Revised October 11, 2011
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, 2007
by 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, 2010
by Yoshio Mimura, Kobe, Japan

2734

27342 = 7474756, a zigzag square.

Page of Squares : First Upload May 7, 2007 ; Last Revised May 7, 2007
by 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.)

Page of Squares : First Upload July 24, 2008 ; Last Revised December 21, 2013
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.

Page of Squares : First Upload May 7, 2007 ; Last Revised May 24, 2011
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, 2008
by 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, 2007
by 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, 2010
by 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, 2011
by Yoshio Mimura, Kobe, Japan

2749

A cubic polynomial :
(X + 8962)(X + 12692)(X + 22682) = X3 + 27492X2 + 37021322X + 25787704322.

Page of Squares : First Upload May 7, 2007 ; Last Revised May 7, 2007
by Yoshio Mimura, Kobe, Japan

2750

27502 = 183 + 1073 + 1853.

Page of Squares : First Upload July 24, 2008 ; Last Revised July 24, 2008
by 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, 2007
by 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, 2013
by 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, 2008
by 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, 2013
by 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)

Page of Squares : First Upload November 4, 2008 ; Last Revised May 24, 2011
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, 2013
by Yoshio Mimura, Kobe, Japan

2757

27572 = 1133 + 1243 + 1623.

Page of Squares : First Upload July 24, 2008 ; Last Revised July 24, 2008
by 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, 2007
by 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, 2008
by Yoshio Mimura, Kobe, Japan

2761

27612 = 25 + 45 + 165 + 175 + 225.

Page of Squares : First Upload July 24, 2008 ; Last Revised July 24, 2008
by 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, 2008
by 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, 2008
by 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, 2013
by 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, 2007
by Yoshio Mimura, Kobe, Japan

2768

27682± 3 are primes.

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by 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, 2007
by 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, 2011
by 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, 2011
by Yoshio Mimura, Kobe, Japan

2774

27742 = (62 + 2)(4502 + 2).

Page of Squares : First Upload May 7, 2007 ; Last Revised December 21, 2013
by 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, 2011
by Yoshio Mimura, Kobe, Japan

2778

27782 = 14 + 134 + 314 + 514.

Page of Squares : First Upload July 24, 2008 ; Last Revised July 24, 2008
by 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, 2014
by Yoshio Mimura, Kobe, Japan

2783

27832 = 114 + 224 + 444 + 444.

Page of Squares : First Upload July 24, 2008 ; Last Revised July 24, 2008
by 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, 2010
by Yoshio Mimura, Kobe, Japan

2787

27872 = 43 + 173 + 1983 = 253 + 1323 + 1763.

Page of Squares : First Upload July 24, 2008 ; Last Revised July 24, 2008
by Yoshio Mimura, Kobe, Japan

2788

27882 = 44 + 84 + 264 + 524.

Page of Squares : First Upload July 24, 2008 ; Last Revised July 24, 2008
by 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, 2011
by 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, 2011
by Yoshio Mimura, Kobe, Japan

2794

27942± 3 are primes.

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

2795

Komachi equations:
27952 = 92 + 82 - 72 + 652 * 432 + 22 - 102 = - 92 - 82 + 72 + 652 * 432 - 22 + 102.

Page of Squares : First Upload September 24, 2010 ; Last Revised September 24, 2010
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)

Page of Squares : First Upload October 9, 2008 ; Last Revised October 9, 2008
by Yoshio Mimura, Kobe, Japan