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4800 - 4899

4800

48002 = 52 + 1952 + 2502.

48002 = (32 - 1)(42 - 1)(92 - 1)(492 - 1) = (92 - 1)(112 - 1)(492 - 1).

Page of Squares : First Upload September 4, 2008 ; Last Revised December 28, 2013
by Yoshio Mimura, Kobe, Japan

4802

48022 = 492 + 492 + 492 + 492 = 72 + 72 + 72 + 72

994k + 1470k + 2338k + 4802k are squares for k = 1,2,3 (982, 56282, 3573082).

Komachi equation: 48022 = 982 * 72 * 62 / 542 * 32 * 212.

Page of Squares : First Upload September 4, 2008 ; Last Revised June 14, 2011
by Yoshio Mimura, Kobe, Japan

4803

48035 = 2556012263502744243 : 252 + 52 + 62 + 02 + 12 + 22 + 22 + 632 + 52 + 02 + 22 + 72 + 42 + 42 + 22 + 42 + 32 = 4803.

Page of Squares : First Upload December 8, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

4804

48042 = 23078416, a square with different digits.

Page of Squares : First Upload October 9, 2007 ; Last Revised October 9, 2007
by Yoshio Mimura, Kobe, Japan

4805

48052 = 1862 + 1862 + 2172.

48052 = (78 + 79 + 80 + 81 + ... + 108)2 + (109 + 110 + 111 + 112 + ... + 139)2 + (140 + 141 + 142 + 143 + ... + 170)2 + ... + (109 + 110 + 111 + 112 + ... + 139)2.

48052 = (52 + 6)(8632 + 6).

Page of Squares : First Upload October 9, 2007 ; Last Revised December 28, 2013
by Yoshio Mimura, Kobe, Japan

4806

48062 = 23097636, 230 * 9 + 76 * 36 = 4806.

48062 = (12 + 2)(22 + 2)(52 + 2)(2182 + 2) = (22 + 2)(402 + 2)(492 + 2) = (222 + 2)(2182 + 2)
= (42 + 2)(52 + 2)(2182 + 2).

Page of Squares : First Upload October 9, 2007 ; Last Revised December 28, 2013
by Yoshio Mimura, Kobe, Japan

4808

48082± 3 are primes.

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

4809

48092± 2 are primes.

Page of Squares : First Upload December 29, 2013 ; Last Revised December 29, 2013
by Yoshio Mimura, Kobe, Japan

4810

48102 = (12 + 1)(22 + 1)(62 + 1)(82 + 1)(312 + 1) = (12 + 1)(62 + 1)(182 + 1)(312 + 1)
= (32 + 1)(62 + 1)(82 + 1)(312 + 1) = (52 + 1)(82 + 1)(1172 + 1)
= (12 + 4)(32 + 4)(122 + 4)(492 + 4).

Page of Squares : First Upload November 2, 2013 ; Last Revised December 28, 2013
by Yoshio Mimura, Kobe, Japan

4811

48112 = 23145721, 23 + 1 * 4 * 57 * 21 = 23 * 1 + 4 * 57 * 21 = 4811.

Page of Squares : First Upload October 9, 2007 ; Last Revised October 9, 2007
by Yoshio Mimura, Kobe, Japan

4812

48122 = 182 + 1332 + 2752

Page of Squares : First Upload September 4, 2008 ; Last Revised September 4, 2008
by Yoshio Mimura, Kobe, Japan

4813

48132 = 23164969, a zigzag square.

Page of Squares : First Upload October 9, 2007 ; Last Revised October 9, 2007
by Yoshio Mimura, Kobe, Japan

4814

48142 = 23174596, a square with different digits.

Page of Squares : First Upload October 9, 2007 ; Last Revised October 9, 2007
by Yoshio Mimura, Kobe, Japan

4816

48162 = 23193856, a zigzag square.

Page of Squares : First Upload October 9, 2007 ; Last Revised October 9, 2007
by Yoshio Mimura, Kobe, Japan

4817

The square root of 4817 is 69.40461..., and 69 = 42 + 02 + 42 + 62 + 12.

Page of Squares : First Upload October 9, 2007 ; Last Revised October 9, 2007
by Yoshio Mimura, Kobe, Japan

4818

48182 = 23213124, a square every digit of which is non-zero and smaller than 5.

48182 = 332 + 802 + 2832

1122k + 1353k + 2508k + 4818k are squares for k = 1,2,3 (992, 57092, 3626372).

Page of Squares : First Upload September 4, 2008 ; Last Revised September 7, 2013
by Yoshio Mimura, Kobe, Japan

4820

48205 = 2601568055043200000 : 22 + 602 + 12 + 52 + 62 + 82 + 02 + 52 + 52 + 02 + 42 + 322 + 02 + 02 + 02 + 02 + 02 = 4820.

Page of Squares : First Upload December 8, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

4823

48232 = 23261329, a zigzag square.

Page of Squares : First Upload October 9, 2007 ; Last Revised October 9, 2007
by Yoshio Mimura, Kobe, Japan

4824

48242 = 722 + 1702 + 2622 = 1442 + 2062 + 2262

48242 = 23270976, and 23 * 270 / 9 * 7 - 6 = 4824.

Page of Squares : First Upload October 9, 2007 ; Last Revised September 4, 2008
by Yoshio Mimura, Kobe, Japan

4825

48252 = 92 + 122 + 122 + 162

48252 = 23280625, a zigzag square.

48252 = 23280625, and 23 + 2 + 80 * 6 * 2 * 5 = 4825.

4825k + 106922k + 110396k + 113098k are squares for k = 1,2,3 (5792, 1908772, 633605492).
960k + 2080k + 2745k + 3240k are squares for k = 1,2,3 (952, 48252, 2541252).

Page of Squares : First Upload October 9, 2007 ; Last Revised June 14, 2011
by Yoshio Mimura, Kobe, Japan

4827

48272 = 23299929, a square consisting of just 3 kinds of digits.

Page of Squares : First Upload October 9, 2007 ; Last Revised October 9, 2007
by Yoshio Mimura, Kobe, Japan

4830

48302 = (12 + 5)(152 + 5)(1302 + 5) = (12 + 5)(52 + 5)(3602 + 5) = (102 + 5)(152 + 5)(312 + 5)
= (32 + 5)(82 + 5)(102 + 5)(152 + 5).

The integral triangle of sides 5307, 8792, 10235 (or 12006, 207001, 219005) has square area 48302.

Page of Squares : First Upload October 14, 2011 ; Last Revised December 28, 2013
by Yoshio Mimura, Kobe, Japan

4832

48302 = (12 + 7)(122 + 7)(1392 + 7).

Page of Squares : First Upload December 28, 2013 ; Last Revised December 28, 2013
by Yoshio Mimura, Kobe, Japan

4833

48332 = 23357889, a square consisting of non decreasing digits.

Page of Squares : First Upload October 9, 2007 ; Last Revised October 9, 2007
by Yoshio Mimura, Kobe, Japan

4834

48342 = 1612 + 2112 + 2142

Loop of length 4 :
4834 --- 482 + 342 = 3460 --- 342 + 602 = 4756 --- 472 + 562 = 5345 --- 532 + 452 = 4834

Page of Squares : First Upload September 4, 2008 ; Last Revised October 9, 2007
by Yoshio Mimura, Kobe, Japan

4836

48362 = 23386896, and 2 * 3 * 38 + 6 * 8 * 96 = 4836.

48362 = (32 + 3)(62 + 3)(112 + 3)(202 + 3).

4836k + 6825k + 8658k + 17706k are squares for k = 1,2,3 (1952, 214112, 25750532).
498k + 942k + 3138k + 3522k are squares for k = 1,2,3 (902, 48362, 2748602).

Page of Squares : First Upload October 9, 2007 ; Last Revised December 28, 2013
by Yoshio Mimura, Kobe, Japan

4839

48392 = 23415921, 234 + 1 * 5 * 921 = 234 * 1 + 5 * 921 = 4839.

Page of Squares : First Upload October 9, 2007 ; Last Revised October 9, 2007
by Yoshio Mimura, Kobe, Japan

4841

48412 = 23435281, and 2 * 34 * 35 * 2 + 81 = 4841.

Page of Squares : First Upload October 9, 2007 ; Last Revised October 9, 2007
by Yoshio Mimura, Kobe, Japan

4844

48442 = 23464336, and 23 * 4 + 6 * 4 * 33 * 6 = 4844.

Page of Squares : First Upload October 9, 2007 ; Last Revised October 9, 2007
by Yoshio Mimura, Kobe, Japan

4848

48482 = 142 + 1622 + 2682 = 162 + 842 + 2842 = 322 + 482 + 522 + 562

48482 = 23503104, and 22 + 32 + 52 + 02 + 32 + 12 + 02 + 42 = 82.

Page of Squares : First Upload October 9, 2007 ; Last Revised September 4, 2008
by Yoshio Mimura, Kobe, Japan

4850

48502± 3 are primes.

48502 = 1072 + 1452 + 2682 = 1322 + 1512 + 2612

Page of Squares : First Upload September 4, 2008 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

4851

48512 = 212 + 1472 + 2732

48512 + 48522 + 48532 + ... + 49002 = 49012 + 49022 + 49032 + ... + 49492.

Page of Squares : First Upload September 4, 2008 ; Last Revised September 16, 2011
by Yoshio Mimura, Kobe, Japan

4852

48525 = 2689081475622188032 : 262 + 82 + 92 + 02 + 82 + 142 + 72 + 562 + 22 + 212 + 82 + 82 + 02 + 32 + 22 = 4852.

Page of Squares : First Upload December 8, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

4854

48542 = 23561316, and 22 + 32 + 52 + 62 + 12 + 32 + 12 + 62 = 112.

Page of Squares : First Upload October 9, 2007 ; Last Revised October 9, 2007
by Yoshio Mimura, Kobe, Japan

4856

48562 = 23580736, and 22 + 32 + 52 + 82 + 02 + 72 + 32 + 62 = 142.

Page of Squares : First Upload October 9, 2007 ; Last Revised October 9, 2007
by Yoshio Mimura, Kobe, Japan

4857

48572 = 42 + 2222 + 2332

Page of Squares : First Upload September 4, 2008 ; Last Revised September 4, 2008
by Yoshio Mimura, Kobe, Japan

4859

48592 = 92 + 1952 + 2532

Page of Squares : First Upload September 4, 2008 ; Last Revised September 4, 2008
by Yoshio Mimura, Kobe, Japan

4860

Komachi equation: 48602 = 92 * 82 / 72 * 62 * 52 / 42 * 32 * 212.

Page of Squares : First Upload September 4, 2008 ; Last Revised October 15, 2010
by Yoshio Mimura, Kobe, Japan

4862

4862 = (12 + 22 + 32 + ... + 413272) / (12 + 22 + 32 + ... + 24392).

48622 = 132 + 372 + 532 + 612

1898k + 4862k + 5954k + 20410k are squares for k = 1,2,3 (1822, 218922, 29723722).
578k + 2074k + 2890k + 4862k are squares for k = 1,2,3 (1022, 60522, 3849482).

48622 = 23639044, 2 + 3 * 6 * 3 * 90 + 4 - 4 = 2 + 3 * 6 * 3 * 90 - 4 + 4
  = 2 + 3 * 6 * 3 * 90 * 4 / 4 = 2 + 3 * 6 * 3 * 90 / 4 * 4 = 4862.

Page of Squares : First Upload October 9, 2007 ; Last Revised June 14, 2011
by Yoshio Mimura, Kobe, Japan


4863

48632± 2 are primes.

Page of Squares : First Upload December 29, 2013 ; Last Revised December 29, 2013
by Yoshio Mimura, Kobe, Japan

4864

The square root of 4864 is 69.742..., and 69 = 72 + 42 + 22.

148644864 = 121922.

Page of Squares : First Upload October 9, 2007 ; Last Revised October 9, 2007
by Yoshio Mimura, Kobe, Japan

4865

48652 = 982 + 2162 + 2332

Page of Squares : First Upload September 4, 2008 ; Last Revised September 4, 2008
by Yoshio Mimura, Kobe, Japan

4866

48662 = 23677956, and 22 + 32 + 62 + 72 + 72 + 92 + 52 + 62 = 172.

Page of Squares : First Upload October 9, 2007 ; Last Revised October 9, 2007
by Yoshio Mimura, Kobe, Japan

4867

48672 = 23687689, 2 * 3 * 6 + 8 + 7 * 689 = 2 * 3 + 6 + 8 * 76 * 8 - 9 = 4867.

48672 = 23687689, and 22 + 32 + 62 + 82 + 72 + 682 + 92 = 22 + 32 + 682 + 72 + 62 + 82 + 92.

48672 = 23687689 appears in the decimal expressions of e:
  e = 2.71828•••23687689••• (from the 33315th digit)
  (23687689 is the eighth 8-digit square in the expression of e.)

Page of Squares : First Upload October 9, 2007 ; Last Revised November 25, 2008
by Yoshio Mimura, Kobe, Japan

4870

48702 = 23716900, and 23716 = 1542, 900 = 302.

Page of Squares : First Upload October 9, 2007 ; Last Revised October 9, 2007
by Yoshio Mimura, Kobe, Japan

4872

48722 = 22 + 262 + 542 + 622

48722 = 23736384, and 22 + 32 + 72 + 32 + 62 + 32 + 82 + 42 = 142.

The integral triangle of sides 19515, 24416, 43877 has square area 48722.

Page of Squares : First Upload October 9, 2007 ; Last Revised October 14, 2011
by Yoshio Mimura, Kobe, Japan

4873

48732 = S2(28) + S2(414), where S2(n) = 12 + 22 + 32 + 42 + ... + n2.

48732 = 42 + 162 + 562 + 612 = 82 + 382 + 472 + 642

Page of Squares : First Upload October 9, 2007 ; Last Revised September 4, 2008
by Yoshio Mimura, Kobe, Japan

4875

The square root of 4875 is 69.821..., and 69 = 82 + 22 + 12.

48752 = (123 + 124 + 125 + 126 + 127)2 + (128 + 129 + 130 + 131 + 132)2 + (133 + 134 + 135 + 136 + 137)2 + ... + (248 + 249 + 250 + 251 + 252)2.

Page of Squares : First Upload October 9, 2007 ; Last Revised October 9, 2007
by Yoshio Mimura, Kobe, Japan

4877

1 / 4877 = 0.0002050440844781628050030, and
20502 + 42 + 40842 + 472 + 82 + 16282 + 05002 + 302 = 48772.

Page of Squares : First Upload October 9, 2007 ; Last Revised October 9, 2007
by Yoshio Mimura, Kobe, Japan

4879

48792 = 23804641, and 238 + 0 + 4641 = 4879.

Page of Squares : First Upload October 9, 2007 ; Last Revised October 9, 2007
by Yoshio Mimura, Kobe, Japan

4880

48802 = 23814400, 2 * 3 * 814 - 4 + 0 + 0 = 2 * 3 * 814 - 4 + 0 * 0 = 4880.

48802= 31 x 32 + 32 x 33 + 33 x 34 + 34 x 35 + 35 x 36 + ... + 414 x 415.

Page of Squares : First Upload October 9, 2007 ; Last Revised October 9, 2007
by Yoshio Mimura, Kobe, Japan

4882

48822 = 23833924, and 22 + 32 + 82 + 32 + 32 + 92 + 22 + 42 = 142.

Page of Squares : First Upload October 9, 2007 ; Last Revised October 9, 2007
by Yoshio Mimura, Kobe, Japan

4885

48855 = 2781780383652053125 : 272 + 82 + 12 + 72 + 82 + 02 + 32 + 82 + 32 + 62 + 52 + 202 + 532 + 12 + 252 = 4885.

Page of Squares : First Upload December 8, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

4886

48862 = 23872996, and 2 + 38 * 7 * 2 * 9 + 96 = 4886.

Page of Squares : First Upload October 9, 2007 ; Last Revised October 9, 2007
by Yoshio Mimura, Kobe, Japan

4888

173 + 4888 = 992, 173 - 4888 = 52.

Page of Squares : First Upload August 2, 2011 ; Last Revised August 2, 2011
by Yoshio Mimura, Kobe, Japan

4890

48903 = 116930169000, and 12 + 12 + 62 + 92 + 32 + 02 + 12 + 692 + 02 + 02 + 02 = 12 + 12 + 692 + 32 + 02 + 12 + 62 + 92 + 02 + 02 + 02 = 4890.

Page of Squares : First Upload December 1, 2008 ; Last Revised December 1, 2008
by Yoshio Mimura, Kobe, Japan

4892

the fifth mosaic square : 48922 = 23931664, 2916 = 542, 3364 = 582.

Page of Squares : First Upload October 9, 2007 ; Last Revised October 9, 2007
by Yoshio Mimura, Kobe, Japan

4894

48942 = 23951236, and 22 + 32 + 92 + 52 + 12 + 22 + 32 + 62 = 132.

Page of Squares : First Upload October 9, 2007 ; Last Revised October 9, 2007
by Yoshio Mimura, Kobe, Japan

4896

48962 = 23970816, a square with different digits.

48962 = (22 + 8)(42 + 8)(142 + 8)(202 + 8) = (22 - 1)(52 - 1)(5772 - 1).

1452 + 4896 = 1612, 1452 - 4896 = 1272.

Page of Squares : First Upload October 9, 2007 ; Last Revised December 28, 2013
by Yoshio Mimura, Kobe, Japan

4897

48972 = 222 + 232 + 382 + 682

Page of Squares : First Upload September 4, 2008 ; Last Revised September 4, 2008
by Yoshio Mimura, Kobe, Japan

4899

48992 = 782 + 2122 + 2412

48992 = 24000201, and 22 + 42 + 02 + 02 + 02 + 22 + 02 + 12 = 52.

Page of Squares : First Upload October 9, 2007 ; Last Revised September 4, 2008
by Yoshio Mimura, Kobe, Japan