1300
13002 = 1690000, 16 = 42 and 90000 = 3002.
13002 = (1 + 2 + 3 + 4)(5)(6 + 7)(8 + 9 + 10 + ... + 72).
13002 = (12 + 1)(32 + 1)(52 + 1)(572 + 1)
= (12 + 1)(32 + 1)(52 + 1)(72 + 1)(82 + 1)
= (12 + 4)(162 + 4)(362 + 4) = (12 + 4)(32 + 4)(42 + 4)(362 + 4)
= (14 + 4)(44 + 4)(64 + 4).
by Yoshio Mimura, Kobe, Japan
1301
13012 = 1692601, 169 = 132 and 2601 = 512.
13012 = 1692601, a reversible square (1062961 = 10312).
13012 = 423 + 563 + 1133.
Page of Squares : First Upload January 22, 2007 ; Last Revised July 7, 2008by Yoshio Mimura, Kobe, Japan
1302
13022 = 1695204, a square with different digits.
13022 = (1)(2)(3 + 4 + 5 + ... + 33)(34 + 35 + 36 + ... + 64).
13022 = (52 + 6)(62 + 6)(362 + 6).
The 4-by-4 magic squares consisting of different squares with constant 1302:
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Page of Squares : First Upload January 22, 2007 ; Last Revised December 14, 2013
by Yoshio Mimura, Kobe, Japan
1303
13032 = 1697809, 1 + 6 * 97 + 80 * 9 = 1303.
The 5-by-5 magic square consisting of different squares with constant 1303:
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Page of Squares : First Upload January 22, 2007 ; Last Revised October 5, 2009
by Yoshio Mimura, Kobe, Japan
1304
13042 = 123 + 763 + 1083.
Page of Squares : First Upload July 7, 2008 ; Last Revised July 7, 2008by Yoshio Mimura, Kobe, Japan
1305
Komachi equation: 13052 = 92 * 872 * 62 / 542 * 32 / 22 * 102.
The 4-by-4 magic square consisting of different squares with constant 1305:
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Page of Squares : First Upload January 25, 2010 ; Last Revised July 23, 2010
by Yoshio Mimura, Kobe, Japan
1306
The sum of the divisors of 13062 is a square, 17292.
Page of Squares : First Upload November 1, 2011 ; Last Revised November 1, 2011by Yoshio Mimura, Kobe, Japan
1307
13072 = 1708249, a square with different digits.
Page of Squares : First Upload January 22, 2007 ; Last Revised January 22, 2007by Yoshio Mimura, Kobe, Japan
1308
Komachi equation: 13082 = 982 / 72 * 6542 * 32 / 212.
Page of Squares : First Upload July 23, 2010 ; Last Revised July 23, 2010by Yoshio Mimura, Kobe, Japan
1311
13112± 2 are primes.
13112 = 1718721, 1 + 7 * 187 + 2 - 1 = 1 * 7 * 187 + 2 * 1 = 1311.
13112 = 1718721, 12 + 72 + 12 + 82 + 72 + 22 + 12 = 132.
A cubic polynomial :
(X + 6082)(X + 13112)(X + 21242) = X3 + 25692X2 + 31712522X + 16930149122.
by Yoshio Mimura, Kobe, Japan
1312
13122 = 44 + 124 + 124 + 364.
Page of Squares : First Upload July 7, 2008 ; Last Revised July 7, 2008by Yoshio Mimura, Kobe, Japan
1314
13142 = 1726596, a zigzag square.
13142± 5 are primes.
106k + 266k + 814k + 1314k are squares for k = 1,2,3 (502, 15722, 531802).
The 4-by-4 magic squares consisting of different squares with constant 1314:
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Page of Squares : First Upload January 22, 2007 ; Last Revised January 16, 2014
by Yoshio Mimura, Kobe, Japan
1316
13162 = 1731856, 1 + 73 * 18 - 5 + 6 = 1316.
Page of Squares : First Upload January 22, 2007 ; Last Revised January 22, 2007by Yoshio Mimura, Kobe, Japan
1317
13172 = 163 + 663 + 1133 = 413 + 783 + 1063.
The 4-by-4 magic squares consisting of different squares with constant 1317:
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Page of Squares : First Upload July 7, 2008 ; Last Revised January 25, 2010
by Yoshio Mimura, Kobe, Japan
1318
82k + 182k + 722k + 1318k are squares for k = 1,2,3 (482, 15162, 516962).
Page of Squares : First Upload April 19, 2011 ; Last Revised April 19, 2011by Yoshio Mimura, Kobe, Japan
1319
1319 is the 9th prime for which the Lendre symbol (a/p) = 1 for a = 1, 2,..., 10
1319 is the third primt for which the Legendre symbol (a/p) = 1 for a = 1, 2,..., 12.
13192 = 1739761, 1 + 7 * 3 * 9 * 7 - 6 + 1 = 1319.
Page of Squares : First Upload January 22, 2007 ; Last Revised January 22, 2007by Yoshio Mimura, Kobe, Japan
1320
612 + 1320 = 712, 612 - 1320 = 492.
13202 = (1)(2)(3)(4)(5)(6 + 7 + 8 + ... + 170),
13202 = (1)(2)(3)(4)(5 + 6 + 7 + ... + 15)(16 + 17 + 18 + ... + 39),
13202 = (1)(2)(3 + 4 + 5 + ... + 8)(9 + 10 + 11)(12 + 13 + 14 + ... + 43),
13202 = (1)(2)(3 + 4 + 5)(6 + 7 + 8 + ... + 10)(11)(12 + 13 + 14 + ... + 21),
13202 = (1)(2 + 3)(4 + 5 + 6 + 7)(8)(9 + 10 + 11 + ... + 63),
13202 = (1 + 2 + 3 + ... + 11)(12)(13 + 14 + 15 + ... + 67),
13202 = (1 + 2 + 3 + ... + 32)(33 + 34 + 35 + ... + 87),
13202 = (1 + 2 + 3 + 4)(5 + 6 + ... + 10)(11 + 12 + ... + 21)(22),
13202 = (1 + 2 + 3 + ... + 9)(10)(11 + 12 + 13 + ... + 21)(22),
13202 = (1 + 2 + 3)(4)(5)(6 + 7 + 8 + ... + 170),
13202 = (1 + 2 + 3)(4)(5 + 6 + 7 + ... + 15)(16 + 17 + 18 + ... + 39).
by Yoshio Mimura, Kobe, Japan
1321
13212 = 1745041, a zigzag square.
Page of Squares : First Upload January 22, 2007 ; Last Revised January 22, 2007by Yoshio Mimura, Kobe, Japan
1322
13222 = 1747684, a zigzag square.
13222 = 13 + 273 + 1203.
Page of Squares : First Upload January 22, 2007 ; Last Revised July 7, 2008by Yoshio Mimura, Kobe, Japan
1323
13232 = 1750329, a square with different digits.
13232 = 1750329, 12 + 72 + 52 + 02 + 32 + 22 + 92 = 132.
Komachi equation: 13232 = 983 / 73 / 63 * 543 - 33 * 213.
13232 = 843 + 1053 = 513 + 633 + 1113.
13232 = (1 + 2 + 3 + 4 + 5 + 6)(7)(8 + 9 + 10 + ... + 154),
13232 = (1 + 2 + 3 + 4 + 5 + 6)(7)(8 + 9 + 10)(11 + 12 +13 + ... + 31).
The 4-by-4 magic squares consisting of different squares with constant 1323:
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Page of Squares : First Upload January 22, 2007 ; Last Revised July 23, 2010
by Yoshio Mimura, Kobe, Japan
1324
13242 = 413 + 793 + 1063.
Page of Squares : First Upload July 7, 2008 ; Last Revised July 7, 2008by Yoshio Mimura, Kobe, Japan
1326
13262 = 1758276, a zigzag square.
13262 = 1758276, 175 * 8 + 2 - 76 = 1326.
13262 = 18 + 18 + 38 + 38 + 48 + 68.
13262 = (1)(2 + 3 + 4)(5 + 6 + 7 + 8)(9 + 10 + 11 + ... + 25)(26).
13262 = 13 + 23 + 33 + 43 + ... + 513.
13262 = (22 + 9)(52 + 9)(632 + 9).
The 4-by-4 magic squares consisting of different squares with constant 1326:
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Page of Squares : First Upload January 22, 2007 ; Last Revised December 14, 2013
by Yoshio Mimura, Kobe, Japan
1328
13282 = 1763584, a square with different digits.
Page of Squares : First Upload January 22, 2007 ; Last Revised January 22, 2007by Yoshio Mimura, Kobe, Japan
1329
13292 = 43 + 893 + 1023.
The 4-by-4 magic square consisting of different squares with constant 1329:
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Page of Squares : First Upload July 7, 2008 ; Last Revised January 25, 2010
by Yoshio Mimura, Kobe, Japan
1330
13302 = (1)(2)(3 + 4)(5 + 6 + 7 + 8 + 9)(10 + 11 + 12 + ... + 85).
13302 = (1)(2)(3 + 4 + ... + 16)(17 + 18 + ... + 116).
1330k + 3610k + 5690k + 6270k are squares for k = 1,2,3 (1302, 93002, 6929002).
1330k + 8417k + 8626k + 10868k are squares for k = 1,2,3 (1712, 162832, 15887612).
510k + 690k + 1330k + 9570k are squares for k = 1,2,3 (1102, 97002, 9377002).
Komachi equation: 13302 = 982 * 762 * 52 / 42 * 32 / 212.
The 4-by-4 magic square consisting of different squares with constant 1330:
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Page of Squares : First Upload January 22, 2007 ; Last Revised April 19, 2011
by Yoshio Mimura, Kobe, Japan
1331
1331 = 113 = 192 + 212 + 232.
13312 = 1213 = 493 + 843 + 1023.
1 / 1331 = 0.00075131480090157776108...,
and 7512 + 312 + 4802 + 092 + 0152 + 7772 + 6102 + 82 = 13312.
13312 = 30 + 32 + 34 + 311 + 313.
Page of Squares : First Upload January 22, 2007 ; Last Revised August 29, 2011by Yoshio Mimura, Kobe, Japan
1332
13322 = 263 + 733 + 1113.
Page of Squares : First Upload July 7, 2008 ; Last Revised July 7, 2008by Yoshio Mimura, Kobe, Japan
1333
Komachi equation: 13332 = 1233 + 453 - 63 - 73 * 83 + 93.
13332 = 463 + 653 + 1123.
74648k + 493210k + 498542k + 710489k are squares for k = 1,2,3 (13332, 10010832, 7765004932).
Page of Squares : First Upload July 7, 2008 ; Last Revised April 19, 2011by Yoshio Mimura, Kobe, Japan
1334
13342 = 1779556, a square with odd digits except the last digit 6.
1334 = (12 + 22 + 32 + ... + 1152) / (12 + 22 + 32 + ... + 102).
Page of Squares : First Upload November 25, 2008 ; Last Revised August 24, 2013by Yoshio Mimura, Kobe, Japan
1335
The 4-by-4 magic square consisting of different squares with constant 1335:
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Page of Squares : First Upload January 25, 2010 ; Last Revised January 25, 2010
by Yoshio Mimura, Kobe, Japan
1336
13362 = 203 + 603 + 1163.
Page of Squares : First Upload July 7, 2008 ; Last Revised July 7, 2008by Yoshio Mimura, Kobe, Japan
1338
(32 + 6)(52 + 6)(72 + 6)(82 + 6) = (13382 + 6),
(12 + 6)(52 + 6)(72 + 6)(122 + 6) = (13382 + 6),
(12 + 6)(22 + 6)(32 + 6)(52 + 6)(72 + 6) = (13382 + 6).
210k + 606k + 762k + 1338k are squares for k = 1,2,3 (542, 16682, 554042).
The 4-by-4 magic squares consisting of different squares with constant 1338:
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Page of Squares : First Upload January 22, 2007 ; Last Revised April 19, 2011
by Yoshio Mimura, Kobe, Japan
1340
13402 = (13 + 9)(53 + 9)(113 + 9).
13402 = 1795600 appears in the decimal expressions of e:
e = 2.71828•••1795600••• (from the 140676th digit)
by Yoshio Mimura, Kobe, Japan
1341
102 + 212 + 322 + 432 + 542 + 652 + ... + 13412 = 86012.
The 4-by-4 magic squares consisting of different squares with constant 1341:
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Page of Squares : First Upload January 22, 2007 ; Last Revised January 25, 2010
by Yoshio Mimura, Kobe, Japan
1342
1342 = (12 + 22 + 32 + ... + 602) / (12 + 22 + 32 + 42 + 52).
13422 = 34 + 174 + 274 + 334.
13422 = 30 + 32 + 34 + 35 + 36 + 37 + 38 + 39 + 311 + 313.
The 4-by-4 magic square consisting of different squares with constant 1342:
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Page of Squares : First Upload July 7, 2008 ; Last Revised August 29, 2011
by Yoshio Mimura, Kobe, Japan
1343
13432 = 1803649, a square with different digits.
Page of Squares : First Upload January 22, 2007 ; Last Revised January 22, 2007by Yoshio Mimura, Kobe, Japan
1344
13442± 5 are primes.
13442 = 883 + 1043.
13442 = (32 - 1)(52 - 1)(972 - 1) = (72 - 1)(132 - 1)(152 - 1).
502 + 1344 = 622, 502 - 1344 = 342.
Komachi equations:
13442 = 12 * 22 / 32 * 42 * 5672 * 82 / 92 = 92 * 82 * 72 / 62 / 52 / 42 * 322 * 102
= 982 / 72 * 62 / 52 / 42 * 322 * 102.
A quartic polynomial: (See 420)
(X + 420)(X + 525)(X + 1344)(X + 1680) = X4 + 632X3 + 23102X2 + 529202X + 7056002.
13442 = (1)(2)(3)(4)(5 + 6 + ... + 11)(12)(13 + 14 + ... + 19),
13442 = (1 + 2 + 3)(4)(5 + 6 + ... + 11)(12)(13 + 14 + ... + 19).
by Yoshio Mimura, Kobe, Japan
1347
13472 = 1! + 2! + 3! + 5 x 9!.
Page of Squares : First Upload March 7, 2007 ; Last Revised March 7, 2007by Yoshio Mimura, Kobe, Japan
1348
13482 = 184 + 244 + 244 + 324.
Page of Squares : First Upload July 7, 2008 ; Last Revised July 7, 2008by Yoshio Mimura, Kobe, Japan
1350
12 + 22 + 32 + 42 + ... + 13502 = 821036475, which consists of distinct digits
(the second 9-digit sum, there are such 2 sums in all).
13502 = 153 + 453 + 1203 = 303 + 653 + 1153.
13502 = (32 + 9)(42 + 9)(62 + 9)(92 + 9) = (62 + 9)(92 + 9)(212 + 9).
Komachi equations:
13502 = 92 * 82 / 72 / 62 * 52 / 42 * 32 * 2102 = 92 / 82 / 72 * 62 * 52 * 42 / 32 * 2102.
The 4-by-4 magic squares consisting of different squares with constant 1350:
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13502 = (1)(2)(3 + 4 + 5 + 6)(7 + 8 + 9 + 10 + 11)(12 + 13)(14 + 15 + 16),
13502 = (1)(2 + 3)(4)(5 + 6 + 7 + 8 + 9 + 10)(11 + 12 + 13 + ... + 64),
13502 = (1)(2 + 3)(4 + 5)(6 + 7 + 8 + 9)(10)(11 + 12 + 13 + ... + 19),
13502 = (1)(2 + 3)(4 + 5 + 6 + 7 + 8)(9)(10)(11 + 12 + 13 + ... + 19),
13502 = (1)(2 + 3)(4 + 5 + 6)(7 + 8)(9 + 10 + 11)(12 + 13 + 14 + 15),
13502 = (1)(2 + 3 + 4 + ... + 10)(11 + 12 + 13 + 14)(15 + 16 + ... + 39),
13502 = (1)(2 + 3 + 4 + ... + 13)(14 + 15 + 16 + ... + 22)(23 + 24 + 25 + 26 + 27),
13502 = (1)(2 + 3 + 4 + ... + 7)(8 + 9 + 10 + 11 + 12)(13 + 14 + 15 + 16 + 17)(18),
13502 = (1)(2 + 3 + 4 + 5 + 6 + 7)(8 + 9 + ... + 367),
13502 = (1)(2 + 3 + 4)(5)(6 + 7 + 8 + 9)(10)(11 + 12 + ... + 19),
13502 = (1 + 2)(3)(4 + 5 + 6 + 7 + 8)(9 + 10 + 11 + ... + 116),
13502 = (1 + 2 + 3 + 4)(5 + 6 + 7)(8 + 9 + 10 + ... + 142),
13502 = (1 + 2 + 3 + 4 + 5)(6 + 7 + ... + 14)(15)(16 + 17 + 18 + 19 + 20),
13502 = (1 + 2 + 3 + 4 + 5)(6 + 7 + 8 + 9)(10 + 11 + ... + 90),
13502 = (1 + 2 + 3 + ... + 9)(10 + 11 + 12 + 13 + 14)(15 + 16 + 17 + ... + 39),
13502 = (1 + 2 + 3 + ... + 9)(10 + 11 + 12 + ... + 17)(18 + 19 + 20 + ... + 32).
by Yoshio Mimura, Kobe, Japan
1351
13512 = 343 + 703 + 1133.
Page of Squares : First Upload July 7, 2008 ; Last Revised July 7, 2008by Yoshio Mimura, Kobe, Japan
1352
1 / 1352 = 0.0007396..., and 7396 = 862.
13522 = 1827904, a square with different digits.
13522 = 264 + 264 + 264 + 264.
13522 = (22 + 4)(4782 + 4).
Page of Squares : First Upload January 22, 2007 ; Last Revised December 14, 2013by Yoshio Mimura, Kobe, Japan
1353
13532 = 483 + 733 + 1103 = 164 + 214 + 224 + 344.
13532 = (192 + 2)(712 + 2).
330k + 1353k + 4026k + 4092k are squares for k = 1,2,3 (992, 59072, 3691712).
1122k + 1353k + 2508k + 4818k are squares for k = 1,2,3 (992, 57092, 3626372).
The 4-by-4 magic squares consisting of different squares with constant 1353:
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Page of Squares : First Upload July 7, 2008 ; Last Revised December 14, 2013
by Yoshio Mimura, Kobe, Japan
1355
13552 = 1836025, a square with different digits.
Page of Squares : First Upload January 22, 2007 ; Last Revised January 22, 2007by Yoshio Mimura, Kobe, Japan
1356
Komachi equations: 13562 = - 95 + 85 - 75 - 65 + 545 / 35 + 25 */ 15 = - 95 + 85 - 75 - 65 + 545 / 35 + 25 / 15.
Page of Squares : First Upload July 23, 2010 ; Last Revised July 23, 2010by Yoshio Mimura, Kobe, Japan
1357
278185k + 298540k + 502090k + 762634k are squares for k = 1,2,3 (13572, 10001092, 7862987232).
Page of Squares : First Upload April 19, 2011 ; Last Revised April 19, 2011by Yoshio Mimura, Kobe, Japan
1358
The 4-by-4 magic squares consisting of different squares with constant 1358:
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Page of Squares : First Upload February 9, 2010 ; Last Revised February 9, 2010
by Yoshio Mimura, Kobe, Japan
1359
The 4-by-4 magic squares consisting of different squares with constant 1359:
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Page of Squares : First Upload February 9, 2010 ; Last Revised February 9, 2010
by Yoshio Mimura, Kobe, Japan
1360
13602 = 63 + 693 + 1153.
13602 = (1)(2 + 3 + 4 + 5 + 6)(7 + 8 + 9 + 10)(11 + 12 + 13 + ... + 74).
13602 = (12 + 4)(22 + 4)(82 + 4)(262 + 4) = (22 + 4)(62 + 4)(762 + 4)
= (22 + 4)(62 + 4)(82 + 4)(92 + 4) = (62 + 4)(82 + 4)(262 + 4).
by Yoshio Mimura, Kobe, Japan
1361
13612 = 1852321, 1 + 85 / 2 * 32 * 1 = 1 * 85 / 2 * 32 + 1 = 1361.
Page of Squares : First Upload January 22, 2007 ; Last Revised January 22, 2007by Yoshio Mimura, Kobe, Japan
1362
290106k + 328242k + 409962k + 826734k are squares for k = 1,2,3 (13622, 10215002, 8329147562).
The 4-by-4 magic squares consisting of different squares with constant 1362:
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Page of Squares : First Upload February 9, 2010 ; Last Revised April 19, 2011
by Yoshio Mimura, Kobe, Japan
1363
13632 = 35 + 75 + 85 + 155 + 165.
Page of Squares : First Upload July 7, 2008 ; Last Revised July 7, 2008by Yoshio Mimura, Kobe, Japan
1364
A cubic polynomial :
(X + 3632)(X + 13642)(X + 20162) = X3 + 24612X2 + 28882922X + 9981861122.
13642 = 1860496, 1860 - 496 = 1364.
Page of Squares : First Upload January 22, 2007 ; Last Revised January 22, 2007by Yoshio Mimura, Kobe, Japan
1365
13652 = 53 + 243 +433 + 623 + 813 + 1003.
13652 = 263 + 423 + 1213 = 263 + 493 + 1203.
Komachi equations:
13652 = 92 * 82 * 72 * 652 / 42 / 32 / 22 */ 12 = 92 / 82 * 72 * 652 * 42 / 32 * 22 */ 12
= 982 / 72 * 652 / 42 * 32 * 22 */ 12.
13652 = (1 + 2)(3 + 4 + 5 + ... + 32)(33 + 34 + 35 + ... + 58),
13652 = (1 + 2 + 3 + 4 + 5 + 6)(7 + 8 + 9 + ... + 32)(33 + 34 + 35 + 36 +37).
13652 = 1682 + 1692 + 1702 + 1712 + 1722 + 1732 + 1742 + ... + 2172.
The 4-by-4 magic squares consisting of different squares with constant 1365:
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Page of Squares : First Upload January 22, 2007 ; Last Revised July 23, 2010
by Yoshio Mimura, Kobe, Japan
1367
13672 = 1868689, a square pegged by 8.
13672 = 105 + 105 + 125 + 175.
Page of Squares : First Upload January 22, 2007 ; Last Revised July 7, 2008by Yoshio Mimura, Kobe, Japan
1368
(12 + 22 + 32 + ... + 1612)(12 + 22 + 32 + ... + 13682) = 346339982.
13682 = (12 + 8)(42 + 8)(72 + 8)(122 + 8).
Komachi equations:
13682 = 92 * 82 * 762 / 52 * 42 / 322 * 102 = 92 / 82 * 762 / 52 / 42 * 322 * 102.
13682 = (1)(2)(3 + 4 + 5 + 6)(7 + 8 + 9 + ... + 12)(13 + 14 + 15 + ... + 44),
13682 = (1)(2)(3 + 4 + 5 + 6)(7 + 8 + 9 + ... + 25)(26 + 27 + 28 + ... + 31),
13682 = (1)(2)(3 + 4 + 5 + 6)(7 + 8 + 9)(10 + 11 + ... + 66),
13682 = (1 + 2)(3 + 4 + 5)(6)(7 + 8 + 9)(10 + 11 + ... + 28).
13682 = 138 * 139 + 139 * 140 + 140 * 141 + ... + 201 * 202.
Page of Squares : First Upload January 22, 2007 ; Last Revised December 14, 2013by Yoshio Mimura, Kobe, Japan
1369
the square of 37.
Loop of length 35 by the function f(N) = ... + c2 + b2 + a2 where N = ... + 1002c + 100b + a:
1369 - 4930 - 3301 - 1090 - ... - 9442 - 10600 - 37 - 1369
(Note f(1369) = 132 + 692 = 4930, f(4930) = 492 + 302 = 3301, etc. See 37)
(12 + 22 + 32 + ... + 7422) + (12 + 22 + 32 + ... + 12922) = (12 + 22 + 32 + ... + 13692).
Page of Squares : First Upload January 22, 2007 ; Last Revised October 9, 2008by Yoshio Mimura, Kobe, Japan
1370
The square root of 1370 is 37.013511....., 37 = 02 + 12 + 32 + 52 + 12 + 12.
Komachi equation: 13702 = 96 + 86 + 76 - 66 + 56 - 46 + 36 + 26 + 106.
Page of Squares : First Upload January 22, 2007 ; Last Revised July 23, 2010by Yoshio Mimura, Kobe, Japan
1371
1371 = 12 + 372 + 12.
1 / 1371 = 0.000729..., 729 = 272.
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 1371:
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Page of Squares : First Upload January 22, 2007 ; Last Revised April 19, 2011
by Yoshio Mimura, Kobe, Japan
1372
13722 = 983 + 983 = 144 + 284 + 284 + 284.
Komachi equations:
13722 = 982 * 72 * 62 * 52 * 42 / 32 / 22 / 102 = 982 * 72 * 62 / 52 / 42 / 32 * 22 * 102
= 982 * 72 / 62 * 52 * 42 * 32 * 22 / 102 = 982 * 72 / 62 / 52 * 42 * 32 / 22 * 102.
by Yoshio Mimura, Kobe, Japan
1374
13742 = 1023 + 55 + 77.
The 4-by-4 magic squares consisting of different squares with constant 1374:
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Page of Squares : First Upload February 9, 2010 ; Last Revised January 6, 2011
by Yoshio Mimura, Kobe, Japan
1375
13752 = 1890625, a square with different digits.
13752 = 15 + 25 + 45 + 185.
The 5-by-5 magic squars consisting of different squares with constant 1375:
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Page of Squares : First Upload January 22, 2007 ; Last Revised October 5, 2009
by Yoshio Mimura, Kobe, Japan
1376
13762 = (52 + 7)(62 + 7)(372 + 7).
Page of Squares : First Upload December 14, 2013 ; Last Revised December 14, 2013by Yoshio Mimura, Kobe, Japan
1377
The first square which is the sum of 4 4-th powers:
13772 = 64 + 12 4 + 214 + 364 = 94 + 184 + 184 + 364 = 144 + 214 + 284 + 324.
13772 = (52 + 2)(2652 + 2).
Page of Squares : First Upload January 22, 2007 ; Last Revised December 14, 2013by Yoshio Mimura, Kobe, Japan
1378
13782± 3 are primes.
13782 = 1898884, a square pegged by 8.
13782 = 13 + 23 + 33 + 43 + 53 + ... + 523.
13782 + 13792 + 13802 + ... + 14042 = 14052 + 14062 + 14072 + ... + 14302.
1378k + 3354k + 4446k + 7722k are squares for k = 1,2,3 (1302, 96202, 7672602).
Page of Squares : First Upload January 22, 2007 ; Last Revised January 16, 2014by Yoshio Mimura, Kobe, Japan
1380
13802 = 93 + 433 + 773 + 1113.
13802 = 643 + 653 + 1113.
13802 = (1)(2)(3)(4 + 5 + 6 + ... + 11)(12 + 13 + 14 + ... + 103),
13802 = (1 + 2 + 3)(4 + 5 + 6 + ... + 11)(12 + 13 + 14 + ... + 103).
18k + 282k + 921k + 1380k are squares for k = 1,2,3 (512, 16832, 585812).
Page of Squares : First Upload January 22, 2007 ; Last Revised April 19, 2011by Yoshio Mimura, Kobe, Japan
1381
13812 = 1907161, a zigzag square.
The square root of 1381 is 37.16...., 37 = 12 + 62.
13812 = 1907161, 12 + 92 + 02 + 72 + 12 + 62 + 12 = 132.
Page of Squares : First Upload January 22, 2007 ; Last Revised January 22, 2007by Yoshio Mimura, Kobe, Japan
1383
The 4-by-4 magic square consisting of different squares with constant 1383:
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Page of Squares : First Upload February 9, 2010 ; Last Revised February 9, 2010
by Yoshio Mimura, Kobe, Japan
1384
1 / 1384 = 0.0007225, 7225 = 852.
Page of Squares : First Upload January 22, 2007 ; Last Revised January 22, 2007by Yoshio Mimura, Kobe, Japan
1386
1386 = (12 + 22 + 32 + ... + 272) / (12 + 22).
The integral triangle of sides 442, 10305, 10549 (or 291, 17545, 17738) has square area 13862.
The 4-by-4 magic squares consisting of different squares with constant 1386:
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13862 = (1)(2)(3 + 4)(5 + 6)(7 + 8 + 9 + ... + 20)(21 + 22 + 23),
13862 = (1)(2)(3 + 4)(5 + 6 + 7 + ... + 16)(17 + 18 + 19 + ... + 49),
13862 = (1)(2)(3 + 4 + 5 + ... + 11)(12 + 13 + 14 + ... + 32)(33),
13862 = (1)(2)(3 + 4 + 5 + ... + 30)(31 + 32)(33),
13862 = (1)(2 + 3 + 4 + ... + 12)(13 + 14 + 15)(16 + 17)(18),
13862 = (1)(2 + 3 + 4 + ... + 5)(6)(7 + 8 + 9 + ... + 15)(16 + 17 + 18 + ... + 26),
13862 = (1)(2 + 3 + 4 + ... + 9)(10 + 11)(12 + 13 + 14 + ... + 65),
13862 = (1)(2 + 3 + 4 + ... + 9)(10 + 11 + 12 + ... + 23)(24 + 25 + 26 + ... + 30),
13862 = (1)(2 + 3 + 4)(5 + 6)(7 + 8 + 9 + ... + 17)(18 + 19 + 20 + ... + 24),
13862 = (1)(2 + 3 + 4)(5 + 6 + 7 + ... + 16)(17 + 18 + 19 + ... + 60),
13862 = (1 + 2)(3)(4)(5 + 6 + 7 + ... + 37)(38 + 39),
13862 = (1 + 2)(3)(4 + 5 + 6 + ... + 59)(60 + 61),
13862 = (1 + 2)(3)(4 + 5 + 6 + ... + 7)(8 + 9 + 10 + ... + 139),
13862 = (1 + 2)(3)(4 + 5 + 6 + ... + 7)(8 + 9 + 10 + ... + 14)(15 + 16 + 17 + ... + 21),
13862 = (1 + 2)(3 + 4)(5 + 6 + 7)(8 + 9 + 10 + 11 + ... + 14)(15 + 16 + 17 + ... + 18),
13862 = (1 + 2)(3 + 4 + 5 + 6)(7)(8 + 9 + 10 + 11 + ... + 14)(15 + 16 + 17 + ... + 18),
13862 = (1 + 2)(3 + 4 + 5 + 6 + 7 + 8)(9 + 10 + 11 + ... + 15)(16 + 17 + 18 + ... + 26),
13862 = (1 + 2 + 3 + ... + 27)(28 + 29 + 30 + ... + 104),
13862 = (1 + 2 + 3 + ... + 7)(8 + 9 + 10 + ... + 370).
by Yoshio Mimura, Kobe, Japan
1387
13872 = 383 + 463 + 1213.
Page of Squares : First Upload July 7, 2008 ; Last Revised July 7, 2008by Yoshio Mimura, Kobe, Japan
1388
13882 = 1926544, 1 * 92 + 6 * 54 * 4 = 1388.
Page of Squares : First Upload January 22, 2007 ; Last Revised January 22, 2007by Yoshio Mimura, Kobe, Japan
1389
The 4-by-4 magic squares consisting of different squares with constant 1389:
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Page of Squares : First Upload February 9, 2010 ; Last Revised February 9, 2010
by Yoshio Mimura, Kobe, Japan
1390
13902 = 563 + 813 + 1073.
The 5-by-5 magic squares consisting of different squares with constant 1390:
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Page of Squares : First Upload July 7, 2008 ; Last Revised October 5, 2009
by Yoshio Mimura, Kobe, Japan
1392
13922 = 1937664, 1 + 9 + 3 * 7 * 66 - 4 = 1392.
13922 = 123 + 793 + 1133 = 483 + 863 + 1063.
Page of Squares : First Upload January 22, 2007 ; Last Revised July 7, 2008by Yoshio Mimura, Kobe, Japan
1393
A cubic polynomial :
(X + 5762)(X + 7442)(X +13932) = X3 + 16812X2 + 13789682X + 5969617922.
by Yoshio Mimura, Kobe, Japan
1394
118490k + 165886k + 748578k + 910282k are squares for k = 1,2,3 (13942, 11960522, 10862689242).
The 4-by-4 magic square consisting of different squares with constant 1394:
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Page of Squares : First Upload February 9, 2010 ; Last Revised April 19, 2011
by Yoshio Mimura, Kobe, Japan
1395
13952 = 1946025, a square with different digits.
The 4-by-4 magic squares consisting of different squares with constant 1395:
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Page of Squares : First Upload January 22, 2007 ; Last Revised February 9, 2010
by Yoshio Mimura, Kobe, Japan
1396
1 / 1396 = 0.00071633237, 72 + 162 + 32 + 322 + 32 + 72 = 1396.
13962 = 1948816, 1 - 9 - 4 + 88 * 16 = 1396.
Page of Squares : First Upload January 22, 2007 ; Last Revised January 22, 2007by Yoshio Mimura, Kobe, Japan
1397
13972 = 1951609, 12 + 92 + 52 + 12 + 62 + 02 + 92 = 152.
13972 = 2272 + 2282 + 2292 + 2302 + 2312 + 2322 + 2332 + ...+2592.
Page of Squares : First Upload January 22, 2007 ; Last Revised January 22, 2007by Yoshio Mimura, Kobe, Japan
1398
The 4-by-4 magic squares consisting of different squares with constant 1398:
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The 5-by-5 magic square consisting of different squares with constant 1398:
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Page of Squares : First Upload October 5, 2009 ; Last Revised February 9, 2010
by Yoshio Mimura, Kobe, Japan
1399
The 5-by-5 magic square consisting of different squares with constant 1399:
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Page of Squares : First Upload October 5, 2009 ; Last Revised October 5, 2009
by Yoshio Mimura, Kobe, Japan