1100
(32 - 8)(42 -8)(52 - 8)(72 - 8)(152 - 8) = (11002 - 8).
55 + 1100 = 652, 55 - 1100 = 452.
11002 = (1 + 2 + ... + 10)(11)(12 + 13)(14 + 15 + ... + 18).
Page of Squares : First Upload December 20, 2006 ; Last Revised July 26, 2011by Yoshio Mimura, Kobe, Japan
1101
11012 = 1212201, which consists of three kinds of digits.
11012 = 1212201, a reversible square (1022121 = 10112).
The 4-by-4 magic square consisting of different squares with constant 1101:
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Page of Squares : First Upload December 20, 2006 ; Last Revised December 14, 2009
by Yoshio Mimura, Kobe, Japan
1102
11022± 3 are primes.
11022 = 1214404, a reversible square (4044121 = 20112).
Page of Squares : First Upload December 20, 2006 ; Last Revised January 16, 2014by Yoshio Mimura, Kobe, Japan
1103
11032 = 1216609, a reversible square (9066121 = 30112).
Page of Squares : First Upload December 20, 2006 ; Last Revised December 20, 2006by Yoshio Mimura, Kobe, Japan
1104
Cubic Polynomials:
(X + 4682)(X + 11042)(X +18172) = X3 + 21772X2 + 22391882X + 9387930242,
(X + 5122)(X + 8372)(X + 11042) = X3 + 14772X2 + 11649122X + 4731125762,
(X + 6282)(X + 11042)(X + 35912) = X3 + 38092X2 + 46133882X + 24896833922.
(12 + 22 + 32 + ... + 1952)(12 + 22 + 32 + ... + 11042) = 334461402.
Page of Squares : First Upload December 20, 2006 ; Last Revised December 20, 2006by Yoshio Mimura, Kobe, Japan
1105
1105 = (12 + 22 + 32 + ... + 252) / (12 + 22).
11052 = (42 + 1)(2682 + 1).
Page of Squares : First Upload November 25, 2008 ; Last Revised November 2, 2013by Yoshio Mimura, Kobe, Japan
1106
13 + 333 + 653 + 973 = 11062 (difference = 32).
The 4-by-4 magic squares consisting of different squares with constant 1106:
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Page of Squares : First Upload December 20, 2006 ; Last Revised December 14, 2009
by Yoshio Mimura, Kobe, Japan
1108
1 / 1108 = 0.0009025, 9025 = 952.
Page of Squares : First Upload December 20, 2006 ; Last Revised December 20, 2006by Yoshio Mimura, Kobe, Japan
1109
11092 = 1229881, 122 + 988 - 1 = 1109.
Page of Squares : First Upload December 20, 2006 ; Last Revised December 20, 2006by Yoshio Mimura, Kobe, Japan
1110
11102 = (12 + 9)(182 + 9)(192 + 9) = (12 + 9)(3512 + 9).
11102 + 34512 = 13141501.
The 4-by-4 magic squares consisting of different squares with constant 1110:
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Page of Squares : First Upload December 20, 2006 ; Last Revised December 14, 2013
by Yoshio Mimura, Kobe, Japan
1111
11112 = 1234321, a palindromic square every digit of which is non-zero and smaller than 5.
Page of Squares : First Upload December 20, 2006 ; Last Revised September 7, 2013by Yoshio Mimura, Kobe, Japan
1112
11122 = 1236544, a reversible square (4456321 = 21112).
11122 = 712 + 732 + 752 + 772 + 782 + 792 + 802 + ... + 1972.
Page of Squares : First Upload December 20, 2006 ; Last Revised January 22, 2007by Yoshio Mimura, Kobe, Japan
1113
11132 = 1238769, a square with different digits.
11132 = 1238769, a reversible square (9678321 = 31112).
11132± 2 are primes.
The 4-by-4 magic squares consisting of different squares with constant 1113:
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Page of Squares : First Upload December 20, 2006 ; Last Revised December 29, 2013
by Yoshio Mimura, Kobe, Japan
1117
11172 = 1247689, a square with different digits.
11172 = 703 + 723 + 813.
Page of Squares : First Upload December 20, 2006 ; Last Revised June 30, 2008by Yoshio Mimura, Kobe, Japan
1119
The 4-by-4 magic squares consisting of different squares with constant 1119:
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Page of Squares : First Upload December 14, 2009 ; Last Revised December 14, 2009
by Yoshio Mimura, Kobe, Japan
1120
Komachi equations:
11202 = 12 * 22 / 32 * 42 * 52 / 62 * 72 * 82 * 92 = 12 / 22 * 32 * 42 * 52 * 62 * 72 * 82 / 92
= 12 * 22 / 32 * 452 * 62 * 72 * 82 / 92 = 92 * 82 * 72 / 62 * 52 * 42 / 32 * 22 */ 12
= 982 / 72 * 62 * 52 * 42 / 32 * 22 */ 12.
11202 = 263 + 563 + 1023.
Page of Squares : First Upload June 30, 2008 ; Last Revised July 20, 2010by Yoshio Mimura, Kobe, Japan
1121
11212 = 1256641, a square with different digits.
11212 = (12 + 22 + 32 + ... + 212) + (12 + 22 + 32 + ... + 1552).
Page of Squares : First Upload December 20, 2006 ; Last Revised December 20, 2006by Yoshio Mimura, Kobe, Japan
1122
11222 = 1258884, a reversible square (4888521 = 22112).
11222 = 1258884, 12 + 5 * 888 / 4 = 1122.
11222 = (1)(2)(3 + 4 + ... + 8)(9 + 10 + ... + 195).
11222 = (12 + 2)(32 + 2)(82 + 2)(242 + 2) = (22 + 2)(192 + 2)(242 + 2) = (32 + 2)(142 + 2)(242 + 2).
1122k + 1353k + 2508k + 4818k are squares for k = 1,2,3 (992, 57092, 3626372).
88k + 638k + 1122k + 1177k are squares for k = 1,2,3 (552, 17492, 574752).
138k + 570k + 1086k + 1122k are squares for k = 1,2,3 (542, 16682, 536762).
The 4-by-4 magic squares consisting of different squares with constant 1122:
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Page of Squares : First Upload December 20, 2006 ; Last Revised December 14, 2013
by Yoshio Mimura, Kobe, Japan
1124
11242 = 1263376, 12 + 22 + 62 + 32 + 32 + 72 + 62 = 122.
11242 = 1263376, 1 * 2 - 6 + 3 * 376 = 1124.
11252 = (1)(2 + 3 + ... + 7)(8 + 9 + ... + 17)(18 + 19 + ... + 32),
11252 = (38 + 39 + 40 + ... + 52)2 + (53 + 54 + 55 + ... + 67)2 + (68 + 69 + 70 + ... + 82)2 + ... + (53 + 54 + 55 + ... + 67)2.
by Yoshio Mimura, Kobe, Japan
1125
11252 = 103 + 173 + 1083 = 753 + 753 + 753.
Page of Squares : First Upload June 30, 2008 ; Last Revised June 30, 2008by Yoshio Mimura, Kobe, Japan
1126
11262 = 643 + 673 + 893.
11262 = 1267876 appears in the decimal expressions of π:
π = 3.14159•••1267876••• (from the 15859th digit)
(1267876 is the second 7-digit square in the expression of π.)
by Yoshio Mimura, Kobe, Japan
1127
11272 = 127(0)129.
11272 = 74 + 144 + 284 + 284.
Page of Squares : First Upload December 20, 2006 ; Last Revised June 30, 2008by Yoshio Mimura, Kobe, Japan
1128
A cubic polynomial:
(X + 11282)(X + 24642)(X + 228692) = X3 + 230292X2 + 620355122X + 635619156482.
11282 = (13 + 23 + 33 + 43 + ... + 473).
Page of Squares : First Upload December 20, 2006 ; Last Revised December 20, 2006by Yoshio Mimura, Kobe, Japan
1129
1129 is the 6th prime for which the Lendre Symbol (a/1129) = 1 for a = 1, 2,..., 10.
11322 = 1281424, 1 * 281 * 4 + 2 * 4 = 1132.
Page of Squares : First Upload December 20, 2006 ; Last Revised December 20, 2006by Yoshio Mimura, Kobe, Japan
1130
11302± 3 are primes.
170k + 370k + 830k + 1130k are squares for k = 1,2,3 (502, 14602, 455002).
Page of Squares : First Upload April 12, 2011 ; Last Revised January 16, 2014by Yoshio Mimura, Kobe, Japan
1133
11332 = 1812 + 1822 + 1832 + 1842 + 1852 + 1862 + 1872 + ... + 2132.
287782k + 295713k + 339900k + 360294k are squares for k = 1,2,3 (11332, 6446772, 3684187432).
Page of Squares : First Upload January 22, 2007 ; Last Revised April 12, 2011by Yoshio Mimura, Kobe, Japan
1134
11342 = (12 + 5)(42 + 5)(1012 + 5) = (112 + 5)(1012 + 5) = (22 + 5)(32 + 5)(1012 + 5)
= (22 + 5)(42 + 5)(72 + 5)(112 + 5).
Komachi equations:
11342 = 122 * 32 * 42 * 5672 / 82 / 92 = 92 / 82 * 72 / 62 / 52 * 4322 * 102.
The 4-by-4 magic squares consisting of different squares with constant 1134:
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11342 = (1)(2)(3)(4 + 5)(6)(7)(8 + 9 + ... + 34),
11342 = (1)(2)(3)(4 + 5)(6)(7 + 8 + ... + 20)(21),
11342 = (1)(2)(3)(4 + 5)(6 + 7 + 8)(9)(10 + 11 + ... + 18),
11342 = (1)(2)(3)(4 + 5)(6 + 7 + 8)(9 + 10 + ... + 12)(13 + 14),
11342 = (1)(2)(3)(4 + 5 + ... + 10)(11 + 12 + ... + 16)(17 + 18 + 19),
11342 = (1)(2)(3 + 4)(5 + 6 + ... + 13)(14 + 15 + ... + 49),
11342 = (1)(2 + 3 + ... + 22)(23 + 24 + ... + 103),
11342 = (1)(2 + 3 + ... + 5)(6)(7)(8 + 9 + 10)(11 + 12 + ... + 16),
11342 = (1)(2 + 3 + ... + 7)(8 + 9 + 10)(11 + 12 + ... + 17)(18),
11342 = (1)(2 + 3 + 4)(5 + 6 + ... + 13)(14)(15 + 16 + ... + 21),
11342 = (1 + 2)(3)(4 + 5)(6)(7)(8 + 9 + ... + 28),
11342 = (1 + 2 + ... + 7)(8 + 9 + ... + 13)(14 + 15 + ... + 40),
11342 = (1 + 2 + 3)(4 + 5)(6)(7)(8 + 9 + ... + 34),
11342 = (1 + 2 + 3)(4 + 5)(6)(7 + 8 + ... + 20)(21),
11342 = (1 + 2 + 3)(4 + 5)(6 + 7 + 8)(9)(10 + 11 + ... + 18),
11342 = (1 + 2 + 3)(4 + 5)(6 + 7 + 8)(9 + 10 + ... + 12)(13 + 14),
11342 = (1 + 2 + 3)(4 + 5 + ... + 10)(11 + 12 + ... + 16)(17 + 18 + 19).
by Yoshio Mimura, Kobe, Japan
1135
11352 = 93 + 663 + 1003.
Page of Squares : First Upload June 30, 2008 ; Last Revised June 30, 2008by Yoshio Mimura, Kobe, Japan
1137
11372 = 1292769, 12 + 22 + 92 + 22 + 72 + 62 + 92 = 162.
11372 = 1292769, 12 * 92 + 7 * 6 - 9 = 1137.
The 4-by-4 magic square consisting of different squares with constant 1137:
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Page of Squares : First Upload December 20, 2006 ; Last Revised December 14, 2009
by Yoshio Mimura, Kobe, Japan
1140
11402 = 43 + 623 + 1023.
Komachi equations:
11402 = 92 * 82 * 762 * 52 / 42 / 32 / 22 */ 12 = 92 / 82 * 762 * 52 * 42 / 32 * 22 */ 12.
The integral triangle of sides 1241, 6884, 8075 has square area 11402.
11402 = (1)(2)(3)(4)(5)(6 + 7 + ... + 9)(10 + 11 + ... + 28),
11402 = (1)(2)(3)(4 + 5 + ... + 8)(9 + 10)(11 + 12 + ... + 29),
11402 = (1)(2)(3 + 4 + ... + 21)(22 + 23 + ... + 78),
11402 = (1)(2)(3 + 4 + ... + 7)(8)(9)(10 + 11 + ... + 28),
11402 = (12)(22)(32 + 42 + ... + 102)(112 + 122 + ... + 152),
11402 = (1 + 2 + 3)(4)(5)(6 + 7 + ... + 9)(10 + 11 + ... + 28),
11402 = (1 + 2 + 3)(4 + 5 + ... + 8)(9 + 10)(11 + 12 + ... + 29).
by Yoshio Mimura, Kobe, Japan
1142
11422 = 1304164, a zigzag square.
Page of Squares : First Upload December 20, 2006 ; Last Revised December 20, 2006by Yoshio Mimura, Kobe, Japan
1143
11432± 2 are primes.
Page of Squares : First Upload December 29, 2013 ; Last Revised December 29, 2013by Yoshio Mimura, Kobe, Japan
1146
11462 = 1313316, a square consisting of three kinds of digits.
11462 = 1313316, a square with odd digits except the last digit 6.
11462 = 54 + 254 + 254 + 274.
The 4-by-4 magic squares consisting of different squares with constant 1146:
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Page of Squares : First Upload December 20, 2006 ; Last Revised August 24, 2013
by Yoshio Mimura, Kobe, Japan
1148
A cubic polynomial:
(X + 10562)(X + 11482)(X + 14492) = X3 + 21292X2 + 25647722 + 17566053122.
by Yoshio Mimura, Kobe, Japan
1149
138k + 417k + 582k + 888k are squares for k = 1,2,3 (452, 11492, 311852).
198777k + 241290k + 291846k + 588288k are squares for k = 1,2,3 (11492, 7273172, 5003561792).
by Yoshio Mimura, Kobe, Japan
1151
1151 is the second prime for which the Lendre Symbol (a/1151) = 1 for a = 1, 2,..., 12.
Page of Squares : First Upload December 20, 2006 ; Last Revised December 20, 2006by Yoshio Mimura, Kobe, Japan
1152
11522 = 244 + 244 + 244 + 244.
11522 = 643 + 165 + 47.
11522 = 1327104 appears in the decimal expressions of π:
π = 3.14159•••1327104••• (from the 50993rd digit)
by Yoshio Mimura, Kobe, Japan
1153
1 / 1153 = 0.00086730268..., 82 + 62 + 72 + 302 + 22 + 62 + 82 = 1153.
11532 = 1329409, 1 + 32 * 9 * 4 + 0 * 9 = 1153.
Page of Squares : First Upload December 20, 2006 ; Last Revised December 20, 2006by Yoshio Mimura, Kobe, Japan
1154
11542 = 1331716, a square with odd digits except the last digit 6.
(11542 - 6) = (42 - 6)(52 - 6)(72 - 6)(132 - 6).
Page of Squares : First Upload December 20, 2006 ; Last Revised August 24, 2013by Yoshio Mimura, Kobe, Japan
1155
A, B, C, A + B, B + C, C + A are squares for (A, B, C) = (11552, 63002, 66882).
11552 = 1334025, 12 + 32 + 32 + 42 + 02 + 22 + 52 = 82.
11552 = (12 + 6)(32 + 6)(72 + 6)(152 + 6).
11552 = 413 + 423 + 1063.
The 4-by-4 magic squares consisting of different squares with constant 1155:
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11552 = (1)(2 + 3)(4 + 5 + ... + 10)(11)(12 + 13 + ... + 33),
11552 = (1)(2 + 3 + 4)(5 + 6)(7)(8 + 9 + ... + 62),
11552 = (1 + 2)(3 + 4)(5)(6 + 7 + ... + 159),
11552 = (1 + 2 + ... + 10)(11 + 12 + ... + 220),
11552 = (1 + 2 + ... + 6)(7 + 8 + ... + 356).
11552 = (29 + 30)2 + (31 + 32)2 + (33 + 34)2 + ... + (125 + 126)2.
Page of Squares : First Upload December 20, 2006 ; Last Revised December 14, 2013by Yoshio Mimura, Kobe, Japan
1156
the square of 34.
11562 = 1336336, which consists of three kinds of digits.
11562 = 1336336, 1 - 33 + 6 * 33 * 6 = 1156.
11562± 3 are primes.
408k + 1156k + 2601k + 3060k are squares for k = 1,2,3 (852, 41992, 2187732).
Page of Squares : First Upload December 20, 2006 ; Last Revised January 16, 2014by Yoshio Mimura, Kobe, Japan
1158
11582 = (12 + 22 + 32 + ... + 342) + (12 + 22 + 32 + ... + 1582).
The 4-by-4 magic square consisting of different squares with constant 1158:
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Page of Squares : First Upload December 20, 2006 ; Last Revised December 25, 2009
by Yoshio Mimura, Kobe, Japan
1160
11602 = (12 + 4)(22 + 4)(52 + 4)(342 + 4) = (12 + 4)(62 + 4)(822 + 4)
= (142 + 4)(822 + 4) = (52 + 4)(62 + 4)(342 + 4).
by Yoshio Mimura, Kobe, Japan
1161
1 / 1161 = 0.000861326...., 82 + 62 + 12 + 322 + 62 = 1161.
The 4-by-4 magic squares consisting of different squares with constant 1161:
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Page of Squares : First Upload December 20, 2006 ; Last Revised December 25, 2009
by Yoshio Mimura, Kobe, Japan
1162
11622 = (12 + 22 + 32 + ... + 1082) + (12 + 22 + 32 + ... + 1402).
11622 = 73 + 383 + 1093.
14k + 1162k + 1274k + 2450k are squares for k = 1,2,3 (702, 29962, 1354362).
Page of Squares : First Upload December 20, 2006 ; Last Revised April 12, 2011by Yoshio Mimura, Kobe, Japan
1164
11642 = 1354896, which consists of different digits.
11642 = 1354896, 13 * 5 / 4 * 8 * 9 - 6 = 1164.
11642 = (12 + 3)(32 + 3)(1682 + 3).
Page of Squares : First Upload December 20, 2006 ; Last Revised December 14, 2013by Yoshio Mimura, Kobe, Japan
1165
11652 = (12 + 4)(5212 + 4).
Page of Squares : First Upload December 14, 2013 ; Last Revised December 14, 2013by Yoshio Mimura, Kobe, Japan
1166
11662 = 1359556, 135 * 9 - 55 + 6 = 1166.
11662 = 1359556, a square with odd digits except the last digit 6.
The 4-by-4 magic square consisting of different squares with constant 1166:
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11662 = 1359556 appears in the decimal expressions of π:
π = 3.14159•••1359556••• (from the 18793rd digit)
(1359556 is the fifth 7-digit square in the expression of π.)
by Yoshio Mimura, Kobe, Japan
1167
11672 = 1361889, 12 + 32 + 62 + 12 + 82 + 82 + 92 = 162.
203058k + 250905k + 387444k + 520482k are squares for k = 1,2,3 (11672, 7247072, 4725754832).
82857k + 275412k + 371106k + 632514k are squares for k = 1,2,3 (11672, 7877252, 5706314912).
The 4-by-4 magic square consisting of different squares with constant 1167:
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Page of Squares : First Upload December 20, 2006 ; Last Revised April 12, 2011
by Yoshio Mimura, Kobe, Japan
1168
A cubic polynomial:
(X + 842)(X + 8192)(X + 11682) = X3 + 14292X2 + 9640682X + 803537282.
by Yoshio Mimura, Kobe, Japan
1169
11692 = 1366561, 12 + 32 + 62 + 62 + 52 + 62 + 12 = 122.
11692 = 243 + 583 + 1053.
Page of Squares : First Upload December 20, 2006 ; Last Revised June 30, 2008by Yoshio Mimura, Kobe, Japan
1170
Komachi equations:
11702 = 92 * 82 * 72 * 652 / 42 * 32 / 212 = 92 * 82 / 72 * 652 / 42 / 32 * 212.
The integral triangle of sides 1053, 2602, 2845 (or 2713, 6088, 8775) has square area 11702.
11702 = (12 + 9)(152 + 9)(242 + 9) = (12 + 9)(22 + 9)(32 + 9)(242 + 9)
= (12 + 9)(22 + 9)(62 + 9)(152 + 9) = (22 + 9)(152 + 9)(212 + 9)
= (22 + 9)(32 + 9)(42 + 9)(152 + 9) = (22 + 9)(32 + 9)(62 + 9)(112 + 9)
= (32 + 9)(112 + 9)(242 + 9) = (32 + 9)(62 + 9)(412 + 9) = (62 + 9)(112 + 9)(152 + 9).
The 4-by-4 magic squares consisting of different squares with constant 1170:
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11702 = (1)(2)(3)(4 + 5 + ... + 16)(17 + 18 + ... + 61),
11702 = (1)(2 + 3)(4)(5)(6 + 7)(8 + 9 + ... + 46),
11702 = (1)(2 + 3)(4 + 5 + ... + 8)(9 + 10 + ... + 17)(18 + 19 + ... + 21),
11702 = (1)(2 + 3 + ... + 6)(7 + 8 + ... + 19)(20 + 21 + ... + 34),
11702 = (1)(2 + 3 + 4)(5 + 6 + ... + 19)(20 + 21 + ... + 45),
11702 = (1)(2 + 3 + 4)(5 + 6 + ... + 8)(9)(10)(11 + 12 + ... + 15),
11702 = (1)(2 + 3 + 4)(5 + 6 + ... + 8)(9 + 10 + ... + 108),
11702 = (1 + 2 + ... + 4)(5 + 6 + ... + 8)(9)(10 + 11 + ... + 35),
11702 = (1 + 2 + ... + 4)(5 + 6 + ... + 8)(9 + 10 + ... + 18)(19 + 20),
11702 = (1 + 2 + 3)(4 + 5 + ... + 16)(17 + 18 + ... + 61).
by Yoshio Mimura, Kobe, Japan
1171
192 + 432 + 672 + 912 + ... + 11712 = 47952 (difference = 24).
11712 = 1371241, 12 + 32 + 72 + 12 + 22 + 42 + 12 = 92.
Page of Squares : First Upload December 20, 2006 ; Last Revised December 20, 2006by Yoshio Mimura, Kobe, Japan
1173
(11732 - 9) = (42 - 9)(52 - 9)(102 - 9)(122 - 9).
1 / 1173 = 0.000852514919..., 82 + 52 + 252 + 12 + 42 + 92 + 192 = 1173.
204k + 294k + 561k + 966k are squares for k = 1,2,3 (452, 11732, 333452).
39882k + 251022k + 418761k + 666264k are squares for k = 1,2,3 (11732, 8269652, 6205439792).
The 4-by-4 magic squares consisting of different squares with constant 1173:
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Page of Squares : First Upload December 20, 2006 ; Last Revised April 12, 2011
by Yoshio Mimura, Kobe, Japan
1174
11742 = 1378276, 1 - 3 + 7 * 8 / 2 * 7 * 6 = 1174,
11742 = 1378276, 137 * 8 + 2 + 76 = 1174.
by Yoshio Mimura, Kobe, Japan
1175
11752 = 1380625, a square with different digits.
11752 = 40 + 42 + 44 + 46 + 48 + 49 + 410.
Page of Squares : First Upload December 20, 2006 ; Last Revised August 29, 2011by Yoshio Mimura, Kobe, Japan
1176
11762 = 1382976, a square with different digits.
11762 = 1382976, 1 + 3 + 8 + 2 * 97 * 6 = 1176.
11762 = (12 + 3)(22 + 3)(32 + 3)(52 + 3)(122 + 3) = (12 + 3)(52 + 3)(92 + 3)(122 + 3)
= (32 + 3)(92 + 3)(372 + 3).
352 + 1176 = 492, 352 - 1176 = 72.
11762 + 11772 + 11782 + ... + 12002 = 12012 + 12022 + 12-32 + ... + 12242.
Komachi equations:
11762 = 12 * 22 / 32 * 42 * 562 * 72 / 82 * 92 = 12 / 22 / 32 / 42 * 562 * 72 * 82 * 92
= 982 * 72 * 62 * 52 * 42 * 32 / 2102 = 982 / 72 / 62 / 52 * 42 * 32 * 2102.
11762 = (1)(2)(3 + 4)(5 + 6 + ... + 11)(12 + 13 + ... + 60),
11762 = (1)(2 + 3 + ... + 5)(6 + 7 + 8)(9 + 10 + ... + 12)(13 + 14 + ... + 19).
11762 = (13 + 23 + 33 + 43 + 53 + ... + 483).
Page of Squares : First Upload December 20, 2006 ; Last Revised December 14, 2013by Yoshio Mimura, Kobe, Japan
1177
11773 = 1630532233, and 12 + 62 + 32 + 02 + 52 + 32 + 22 + 22 + 332 = 1177.
88k + 638k + 1122k + 1177k are squares for k = 1,2,3 (552, 17492, 574752).
1177k + 376640k + 426074k + 581438k are squares for k = 1,2,3 (11772, 8133072, 5721408772).
by Yoshio Mimura, Kobe, Japan
1178
11782 = 194 + 214 + 274 + 274.
The 4-by-4 magic square consisting of different squares with constant 1178:
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Page of Squares : First Upload June 30, 2008 ; Last Revised December 25, 2009
by Yoshio Mimura, Kobe, Japan
1179
The 4-by-4 magic square consisting of different squares with constant 1179:
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Page of Squares : First Upload December 25, 2009 ; Last Revised December 25, 2009
by Yoshio Mimura, Kobe, Japan
1180
the square root of 1180 is 34. 3 5 ..., 34 = 32 + 52.
Page of Squares : First Upload December 20, 2006 ; Last Revised December 20, 2006by Yoshio Mimura, Kobe, Japan
1181
11812 = 1394761, 13 * 94 - 7 * 6 + 1 = 1181.
Page of Squares : First Upload December 20, 2006 ; Last Revised December 20, 2006by Yoshio Mimura, Kobe, Japan
1182
12 + 22 + 32 + 42 + ... + 11822 = 551165615, which consists of 3 kinds of digits.
11822 = 93 + 593 + 1063.
The 4-by-4 magic squares consisting of different squares with constant 1182:
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Page of Squares : First Upload December 20, 2006 ; Last Revised December 25, 2009
by Yoshio Mimura, Kobe, Japan
1183
11832 = 1399489, 139 * 9 + 4 - 8 * 9 = 1183.
11832 = 653 + 1043 = 134 + 264 + 264 + 264.
Page of Squares : First Upload December 20, 2006 ; Last Revised June 30, 2008by Yoshio Mimura, Kobe, Japan
1184
1184 = (12 + 22 + 32 + ... + 7032) / (12 + 22 + 32 + ... + 662).
Page of Squares : First Upload November 25, 2008 ; Last Revised November 25, 2008by Yoshio Mimura, Kobe, Japan
1185
The 4-by-4 magic square consisting of different squares with constant 1185:
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Page of Squares : First Upload December 25, 2009 ; Last Revised December 25, 2009
by Yoshio Mimura, Kobe, Japan
1186
11862 = 1406596, a zigzag square.
11862 = 1406596, 1 + 40 * 6 * 5 - 9 - 6 = 1186.
Page of Squares : First Upload December 20, 2006 ; Last Revised December 20, 2006by Yoshio Mimura, Kobe, Japan
1188
11882 = 1411344, which consists of 3 kinds of digit.
1 / 1188 = 0.000841..., 841 = 292.
11882 = 1411344, a square every digit of which is non-zero and smaller than 5.
11882 = (12 + 8)(102 + 8)(382 + 8) = (12 + 8)(22 + 8)(62 + 8)(172 + 8)
= (12 + 8)(52 + 8)(62 + 8)(102 + 8) = (22 + 2)(42 + 2)(82 + 2)(142 + 2) = (62 + 8)(102 + 8)(172 + 8).
190k + 338k + 786k + 802k are squares for k = 1,2,3 (462, 11882, 323562).
11882 = (1)(2)(3 + 4 + ... + 8)(9 + 10 + ... + 35)(36),
11882 = (1)(2 + 3 + ... + 10)(11)(12)(13 + 14 + ... + 23),
11882 = (1)(2 + 3 + ... + 97)(98 + 99 + 100),
11882 = (1 + 2)(3 + 4 + ... + 6)(7 + 8 + ... + 17)(18 + 19 + ... + 26),
11882 = (1 + 2)(3 + 4 + 5)(6)(7 + 8 + ... + 114),
11882 = (1 + 2 + ... + 11)(12)(13 + 14)(15 + 16 + ... + 18),
11882 = (1 + 2 + ... + 8)(9)(10 + 11 + 12)(13 + 14 + ... + 20).
by Yoshio Mimura, Kobe, Japan
1189
1 + 2 + 3 + 4 + 5 + 6 + ... + 1681 = 11892.
16812 - 16802 - 16792 + 16782 - ... + 12 = 11892.
11892 = 1 + 2 + ... + 1681 = 13 + 23 + 33 + 43 + 53 + 63 + ... + 573.
1 / 1189 = 0.000841..., 841 = 292.
11892 = (12 + 22 + 32 + 42 + ... + 8402) / (12 + 22 + 32 + 42 + ... 72).
11892 = 1413721, 12 + 42 + 12 + 32 + 72 + 22 + 12 = 92.
299628k + 306762k + 382858k + 424473k are squares for k = 1,2,3 (11892, 7145892, 4340123472).
Page of Squares : First Upload December 20, 2006 ; Last Revised April 12, 2011by Yoshio Mimura, Kobe, Japan
1190
11902 = (1)(2)(3 + 4 + ... + 7)(8 + 9)(10 + 11 + ... + 58),
11902 = (1)(2 + 3 + ... + 8)(9 + 10 + ... + 25)(26 + 27 + ... + 30).
Komachi equation: 11902 = 122 * 342 * 52 * 62 * 72 / 82 / 92.
The 4-by-4 magic squares consisting of different squares with constant 1190:
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Page of Squares : First Upload December 20, 2006 ; Last Revised July 20, 2010
by Yoshio Mimura, Kobe, Japan
1191
11912 = 2262 + 6862 + 9472 = 7492 + 6862 + 6222.
Page of Squares : First Upload September 7, 2013 ; Last Revised September 7, 2013by Yoshio Mimura, Kobe, Japan
1193
the square root of 1193 is 34. 5 3..., and 34 = 52 + 32.
Page of Squares : First Upload December 20, 2006 ; Last Revised December 20, 2006by Yoshio Mimura, Kobe, Japan
1194
42k + 129k + 660k + 1194k are squares for k = 1,2,3 (452, 13712, 446312).
The 4-by-4 magic squares consisting of different squares with constant 1194:
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Page of Squares : First Upload December 25, 2009 ; Last Revised April 12, 2011
by Yoshio Mimura, Kobe, Japan
1196
11962± 3 are primes.
11962 = (12 + 22 + 32 +42 + 52 + 62) + (12 + 22 + 32 + 42 + ... + 1622).
Page of Squares : First Upload December 20, 2006 ; Last Revised January 16, 2014by Yoshio Mimura, Kobe, Japan
1197
11972 = 1432809, a square with different digits.
11972 = (1 + 2 + ... + 6)(7 + 8 + ... + 12)(13 + 14 + ... + 50).
The 4-by-4 magic squares consisting of different squares with constant 1197:
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Page of Squares : First Upload December 20, 2006 ; Last Revised December 25, 2009
by Yoshio Mimura, Kobe, Japan