4900
The square of 70.
49002 = 352 + 2102 + 2452 = 812 + 1672 + 2662
Komachi equations:
49002 = 14 * 24 * 34 * 44 * 54 * 64 * 74 / 84 / 94 = 14 * 24 / 34 / 44 * 54 / 64 * 74 * 84 * 94
= 14 / 24 * 34 / 44 * 54 * 64 * 74 * 84 / 94 = 14 / 24 * 34 * 454 / 64 * 74 * 84 / 94
= 94 * 84 * 74 / 64 * 54 / 44 / 34 * 24 */ 14 = 984 / 74 * 64 * 54 / 44 / 34 * 24 */ 14
= 984 / 74 / 64 * 54 * 44 * 34 / 24 */ 14.
by Yoshio Mimura, Kobe, Japan
4901
49012=24019801, and 2401 = 492, 9801 = 992.
The square root of 4901 is 70.007142..., and 70 = 02 + 02 + 72 + 12 + 42 + 22.
49012 = (254 + 255 + 256 + ... + 266)2 + (267 + 268 + 269 + ... + 279)2.
Page of Squares : First Upload October 15, 2007 ; Last Revised October 15, 2007by Yoshio Mimura, Kobe, Japan
4902
49022 = 822 + 2092 + 2432
Page of Squares : First Upload September 4, 2008 ; Last Revised September 4, 2008by Yoshio Mimura, Kobe, Japan
4903
1 / 4903 = 0.00020395676116, 22 + 02 + 392 + 562 + 72 + 62 + 112 + 62 = 4903,
1 / 4903 = 0.00020395676116, 22 + 0392 + 562 + 72 + 62 + 112 + 62 = 4903.
by Yoshio Mimura, Kobe, Japan
4904
49042 = 42 + 1282 + 2802
Page of Squares : First Upload September 4, 2008 ; Last Revised September 4, 2008by Yoshio Mimura, Kobe, Japan
4906
49062 = 24068836, and 2 + 4068 + 836 = 4906.
Page of Squares : First Upload October 15, 2007 ; Last Revised October 15, 2007by Yoshio Mimura, Kobe, Japan
4907
49075 = 2844987023923141307 : 22 + 82 + 42 + 492 + 82 + 72 + 02 + 22 + 392 + 232 + 142 + 12 + 32 + 02 + 72 = 4907.
Page of Squares : First Upload December 8, 2008 ; Last Revised December 8, 2008by Yoshio Mimura, Kobe, Japan
4908
49082± 5 are primes.
49082 = 182 + 1522 + 2742
49082 = 24088464, a square with even digits.
Page of Squares : First Upload October 15, 2007 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
4913
49132 = 572 + 1262 + 2802 = 42 + 262 + 562 + 612 = 82 + 222 + 442 + 672 = 82 + 462 + 472 + 622 = 172 + 342 + 342 + 682
49132 = 24137569, a square with different digits.
Loop of length 56 by the function f(N) = ... + c2 + b2 + a2 where N = ... + 1002c + 100b + a:
4913 - 2570 - 5525 - 3650 - ... - 41 - 1681 - 6817 - 4913
(Note f(4913) = 492 + 132 = 2570, f(2570) = 252 + 702 = 5525, etc. See 41)
A cubic polynomial :
(X + 19202)(X + 27372)(X + 36002) = X3 + 49132X2 + 131330402X + 189181440002.
49132 is the first sum of four 4th powers in four ways:
49132 = 44 + 264 + 564 + 614 = 84 + 224 + 444 + 674 = 84 + 464 + 474 + 624
= 174 + 344 + 344 + 684.
by Yoshio Mimura, Kobe, Japan
4914
49142 = 813 + 823 + 833 + 843 + 853 + 863 + ... + 1083.
Komachi equation: 49142 = 92 * 82 * 72 * 652 / 42 * 32 * 22 / 102.
Page of Squares : First Upload November 25, 2008 ; Last Revised October 15, 2010by Yoshio Mimura, Kobe, Japan
4915
49152 = 182 + 242 + 2892
Page of Squares : First Upload September 4, 2008 ; Last Revised September 4, 2008by Yoshio Mimura, Kobe, Japan
4916
49162 = 32 + 82 + 132 + 262 + 262
Page of Squares : First Upload September 4, 2008 ; Last Revised September 4, 2008by Yoshio Mimura, Kobe, Japan
4917
4917 = (12 + 22 + 32 + ... + 2972) / (12 + 22 + 32 + ... + 172).
Page of Squares : First Upload November 25, 2008 ; Last Revised November 25, 2008by Yoshio Mimura, Kobe, Japan
4918
49182 = 24186724, a zigzag square.
Page of Squares : First Upload October 15, 2007 ; Last Revised October 15, 2007by Yoshio Mimura, Kobe, Japan
4920
49202 = 162 + 682 + 2882 = 1062 + 1982 + 2482
The square root of 4920 is 70.1427..., and 70 = 12 + 42 + 22 + 72.
Page of Squares : First Upload October 15, 2007 ; Last Revised September 4, 2008by Yoshio Mimura, Kobe, Japan
4922
49222 = 12 + 1162 + 2832
49222 = 24226084, and 22 + 42 + 22 + 22 + 62 + 02 + 82 + 42 = 122.
49222 = 24226084, a square consisting of even digits.
Page of Squares : First Upload October 15, 2007 ; Last Revised September 4, 2008by Yoshio Mimura, Kobe, Japan
4924
49242± 3 are primes.
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
4928
49282± 3 are primes.
49282 = 24285184, 24 / 2 * 8 * 51 + 8 * 4 = 4928.
49282 = (22 + 7)(52 + 7)(72 + 7)(352 + 7) = (22 + 7)(72 + 7)(92 + 7)(212 + 7)
= (72 + 7)(212 + 7)(312 + 7).
by Yoshio Mimura, Kobe, Japan
4929
49292 = 22 + 542 + 2892
Page of Squares : First Upload September 4, 2008 ; Last Revised September 4, 2008by Yoshio Mimura, Kobe, Japan
4930
4930 = (12 + 22 + 32 + ... + 1442) / (12 + 22 + 32 + ... + 82).
49302 = (12 + 1)(22 + 1)(382 + 1)(412 + 1) = (22 + 1)(42 + 1)(132 + 1)(412 + 1)
= (32 + 1)(382 + 1)(412 + 1) = (52 + 4)(82 + 4)(1112 + 4)
= (12 + 9)(15592 + 9) = (42 + 9)(52 + 9)(72 + 9)(222 + 9) = (72 + 9)(222 + 9)(292 + 9).
4930k + 11078k + 15254k + 22562k are squares for k = 1,2,3 (2322, 298122, 40637122).
Loop of length 35 by the function f(N) = ... + c2 + b2 + a2 where N = ... + 1002c + 100b + a:
4930 - 3301 - 1090 - 8200 - ... - 10600 - 37 - 1369 - 4930
(Note f(4930)= 492 + 302 = 3301, f(3301) = 332 + 012 = 1090, etc. See 37)
by Yoshio Mimura, Kobe, Japan
4931
49312 = 24314761 appears in the decimal expressions of e:
e = 2.71828•••24314761••• (from the 41740th digit)
(24314761 is the tenth 8-digit square in the expression of e.)
by Yoshio Mimura, Kobe, Japan
4932
49322 = 1862 + 1962 + 2182 = 122 + 122 + 482 + 662
49325 = 2918201925080466432 : 292 + 182 + 202 + 12 + 92 + 22 + 52 + 02 + 82 + 02 + 462 + 62 + 42 + 322 = 4932.
Page of Squares : First Upload September 4, 2008 ; Last Revised December 8, 2008by Yoshio Mimura, Kobe, Japan
4935
49352 = 212 + 1792 + 2652
Komachi equations:
49352 = 9872 * 62 * 52 / 42 / 32 * 22 */ 12 = 9872 / 62 * 52 * 42 * 32 / 22 */ 12.
by Yoshio Mimura, Kobe, Japan
4936
1 / 4936 = 0.0002025, 2025 = 452. (also 4937 and 4938)
Page of Squares : First Upload October 15, 2007 ; Last Revised October 15, 2007by Yoshio Mimura, Kobe, Japan
4937
49372 = 24373969, a zigzag square.
Page of Squares : First Upload October 15, 2007 ; Last Revised October 15, 2007by Yoshio Mimura, Kobe, Japan
4940
2812k + 4940k + 8056k + 13433k are squares for k = 1,2,3 (1712, 166632, 17577092).
Page of Squares : First Upload June 17, 2011 ; Last Revised June 17, 2011by Yoshio Mimura, Kobe, Japan
4941
49412 = 1112 + 2112 + 2392 = 1842 + 1852 + 2282
49412 = 13 - 23 + 33 - 43 + 53 - 63 + ... +3633 - 3643 + 3653.
Page of Squares : First Upload October 15, 2007 ; Last Revised September 4, 2008by Yoshio Mimura, Kobe, Japan
4944
49442 = 1322 + 2082 + 2362
Page of Squares : First Upload September 4, 2008 ; Last Revised September 4, 2008by Yoshio Mimura, Kobe, Japan
4946
49462 = 24462916, and 2446 * 2 + 9 * 1 * 6 = 4946.
Page of Squares : First Upload October 15, 2007 ; Last Revised October 15, 2007by Yoshio Mimura, Kobe, Japan
4947
1 / 4947 = 0.00020214271275520, 202 + 22 + 142 + 272 + 122 + 72 + 552 + 202 = 4947.
Page of Squares : First Upload October 15, 2007 ; Last Revised October 15, 2007by Yoshio Mimura, Kobe, Japan
4948
49482 = 24482704, and 22 + 42 + 42 + 82 + 22 + 72 + 02 + 42 = 132.
Page of Squares : First Upload October 15, 2007 ; Last Revised October 15, 2007by Yoshio Mimura, Kobe, Japan
4949
49492 = 24492601, and 24 + 4926 + 0 - 1 = 4949.
Page of Squares : First Upload October 15, 2007 ; Last Revised October 15, 2007by Yoshio Mimura, Kobe, Japan
4950
49502 = 1292 + 2192 + 2282
The square root of 4950 is 70.356..., and 70 = 32 + 52 + 62.
49502 = 24502500, 2450 * 2 + 50 + 0 = 2450 + 2500 = 4950.
Page of Squares : First Upload October 15, 2007 ; Last Revised September 4, 2008by Yoshio Mimura, Kobe, Japan
4955
49554 = 602801931600625, and 602 + 22 + 82 + 02 + 192 + 32 + 162 + 02 + 02 + 62 + 252 = 4955.
Page of Squares : First Upload December 1, 2008 ; Last Revised December 1, 2008by Yoshio Mimura, Kobe, Japan
4957
49572 = 24571849, and 22 + 42 + 52 + 72 + 12 + 82 + 42 + 92 = 162.
Page of Squares : First Upload October 15, 2007 ; Last Revised October 15, 2007by Yoshio Mimura, Kobe, Japan
4966
49662 = 42 + 62 + 142 + 252 + 272
Page of Squares : First Upload September 4, 2008 ; Last Revised September 4, 2008by Yoshio Mimura, Kobe, Japan
4967
49672 = 82 + 142 + 462 + 672
49672 = 24671089, a square with different digits.
Page of Squares : First Upload October 15, 2007 ; Last Revised September 4, 2008by Yoshio Mimura, Kobe, Japan
4971
49712 = 1802 + 1842 + 2332
Page of Squares : First Upload September 4, 2008 ; Last Revised September 4, 2008by Yoshio Mimura, Kobe, Japan
4972
49722 = 52 + 62 + 112 + 122 + 302
1 / 4972 = 0.000201126307320, 202 + 12 + 122 + 632 + 02 + 72 + 32 + 202 = 4972,
1 / 4972 = 0.000201126307320, 202 + 12 + 122 + 632 + 072 + 32 + 202 = 4972.
by Yoshio Mimura, Kobe, Japan
4973
Loop of length 6 by the function f(N) = ... + c2 + b2 + a2 where N = ... + 1002c + 100b + a:
4973 -- 7730 -- 6829 -- 5465 -- 7141 -- 6722 -- 4973
(Note f(4973) = 492 + 732 = 7730, f(7730) = 772 + 302 = 6829, etc. See 41)
by Yoshio Mimura, Kobe, Japan
4976
49762= 112 x 113 + 113 x 114 + 114 x 115 + 115 x 116 + ... + 422 x 423.
Page of Squares : First Upload October 15, 2007 ; Last Revised October 15, 2007by Yoshio Mimura, Kobe, Japan
4977
49772 = 24770529, and 24 + 7 * 705 + 2 * 9 = 4977.
Page of Squares : First Upload October 15, 2007 ; Last Revised October 15, 2007by Yoshio Mimura, Kobe, Japan
4978
49782 = 192 + 862 + 2892 = 812 + 1712 + 2682
2242k + 4978k + 13262k + 15618k are squares for k = 1,2,3 (1902, 212042, 25053402).
Page of Squares : First Upload September 4, 2008 ; Last Revised June 17, 2011by Yoshio Mimura, Kobe, Japan
4980
The quadratic polynomial -4980X2 + 42060X - 34271 takes the values 532, 1732, 2172, 2332, 2272, 1972, 1272 at X = 1, 2,..., 7,
Page of Squares : First Upload December 15, 2008 ; Last Revised December 15, 2008by Yoshio Mimura, Kobe, Japan
4983
49832 = 662 + 742 + 2892 = 1132 + 1982 + 2502
Page of Squares : First Upload September 4, 2008 ; Last Revised September 4, 2008by Yoshio Mimura, Kobe, Japan
4985
49852 = 252 + 1862 + 2642 = 812 + 1872 + 2612
Page of Squares : First Upload September 4, 2008 ; Last Revised September 4, 2008by Yoshio Mimura, Kobe, Japan
4986
49862± 5 are primes.
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
4987
49872 = 24870169, a square with different digits.
A cubic polynomial :
(X + 15042)(X + 26882)(X + 38072) = X3 + 48972X2 + 124034882X + 153907568642.
by Yoshio Mimura, Kobe, Japan
4988
1505k + 4042k + 4988k + 6106k are squares for k = 1,2,3 (1292, 89872, 6489992).
1 / 4988 = 0.0002004811547714, 22 + 02 + 0482 + 12 + 152 + 472 + 72 + 142 = 4988,
1 / 4988 = 0.0002004811547714, 22 + 002 + 482 + 12 + 152 + 472 + 72 + 142 = 4988,
1 / 4988 = 0.0002004811547714, 22 + 00482 + 12 + 152 + 472 + 72 + 142 = 4988.
by Yoshio Mimura, Kobe, Japan
4992
49922 = 1002 + 1562 + 2722 = 1282 + 2082 + 2402
Page of Squares : First Upload September 4, 2008 ; Last Revised September 4, 2008by Yoshio Mimura, Kobe, Japan
4998
Komachi equation: 49982 = 982 * 7652 * 42 / 32 / 22 / 102.
4998k + 6468k + 10542k + 13713k are squares for k = 1,2,3 (1892, 191312, 20360972).
4998k + 6888k + 8106k + 15729k are squares for k = 1,2,3 (1892, 196352, 22080872).
by Yoshio Mimura, Kobe, Japan
4999
49993 = 124925014999, and 12 + 22 + 492 + 22 + 52 + 02 + 12 + 492 + 92 + 92 = 4999.
Page of Squares : First Upload December 1, 2008 ; Last Revised December 1, 2008by Yoshio Mimura, Kobe, Japan