1200
A cubic polynomial:
(X + 5672)(X + 12002)(X + 15402) = X3 + 20332X2 + 21541802X + 10478160002.
12002 = (1)(2 + 3)(4)(5 + 6 + ... + 379),
12002 = (1 + 2 + 3 + 4)(5 + 6 + 7 + ... + 19)(20 + 21 + 22 + ... + 44),
12002 = (1 + 2 + 3 + 4 + 5)(6 + 7 + 8 + 9 + 10)(11 + 12 + 13 + 14)(15 + 16 + 17).
by Yoshio Mimura, Kobe, Japan
1201
12012 = 1442401, a reversible square (1042441 = 10212).
12012 = 1442401, 144 = 122, 2401 = 492.
1201 is the 8th prime so that the Legendre symbol (a/p) = 1 for a = 1,2,...,10.
12012 = 1442401 appears in the decimal expressions of e:
e = 2.71828•••1442401••• (from the 90607th digit)
by Yoshio Mimura, Kobe, Japan
1202
12022 = 1444804, a reversible square (4084441 = 20212).
Page of Squares : First Upload January 16, 2007 ; Last Revised January 16, 2007by Yoshio Mimura, Kobe, Japan
1203
12032 = 63 + 163 + 1133 = 443 + 813 + 943.
Page of Squares : First Upload June 30, 2008 ; Last Revised June 30, 2008by Yoshio Mimura, Kobe, Japan
1205
12052 = 13 + 613 + 1073.
Page of Squares : First Upload June 30, 2008 ; Last Revised June 30, 2008by Yoshio Mimura, Kobe, Japan
1206
The 4-by-4 magic squares consisting of different squares with constant 1206:
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Page of Squares : First Upload January 6, 2010 ; Last Revised January 6, 2010
by Yoshio Mimura, Kobe, Japan
1207
62764k + 451418k + 470730k + 471937k are squares for k = 1,2,3 (12072, 8074832, 5492320732).
66385k + 115872k + 569704k + 704888k are squares for k = 1,2,3 (12072, 9161132, 7327950472).
12072 = 1456849 appears in the decimal expressions of e:
e = 2.71828•••1456849••• (from the 54620th digit)
by Yoshio Mimura, Kobe, Japan
1209
29016k + 175305k + 570648k + 686712k are squares for k = 1,2,3 (12092, 9103772, 7176853712).
The 4-by-4 magic squares consisting of different squares with constant 1209:
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Page of Squares : First Upload January 6, 2010 ; Last Revised April 15, 2011
by Yoshio Mimura, Kobe, Japan
1210
12102 = 93 + 623 + 1073.
12102 = (1 + 2 + 3 + 4)(5)(6 + 7 + 8 + ... + 16)(17 + 18 + 19 + ... + 27).
Page of Squares : First Upload January 16, 2007 ; Last Revised June 30, 2008by Yoshio Mimura, Kobe, Japan
1211
A cubic polynomial:
(X + 9122)(X + 12112)(X + 18362) = X3 + 23812X2 + 29944922X + 20277371522.
12112 = 1466521 is a reversible square (1256641 = 11212).
Page of Squares : First Upload January 16, 2007 ; Last Revised January 16, 2007by Yoshio Mimura, Kobe, Japan
1212
12122 = 1468944 is a reversible square (4498641 = 21212).
12122± 5 are primes.
12122 = 164 + 244 + 264 + 284.
Page of Squares : First Upload January 16, 2007 ; Last Revised January 16, 2014by Yoshio Mimura, Kobe, Japan
1215
Komachi equation: 12152 = 92 / 82 / 72 * 62 * 52 * 42 * 32 * 212.
12152 = (1)(2 + 3 + ... + 7)(8 + 9 + ... + 22)(23 + 24 + ... + 31).
12152 = (1)(2 + 3 + ... + 7)(8 + 9 + 10)(11 + 12 + ... + 64).
Page of Squares : First Upload January 16, 2007 ; Last Revised July 20, 2010by Yoshio Mimura, Kobe, Japan
1218
12182 = 1483524 , 14 * 83 + 52 + 4 = 1218.
12182± 5 are primes.
12182 = 14 + 134 + 274 + 314.
59682k + 337386k + 434826k + 651630k are squares for k = 1,2,3 (12182, 8550362, 6304977002).
12182 = (1 + 2 + ... + 28)(29)(30 + 31 + ... + 33).
12182 = (1 + 2 + ... + 6)(7 + 8 + ... + 14)(15 + 16 + ... + 43).
12182 = (172 + 5)(712 + 5) = (32 + 5)(42 + 5)(712 + 5) = (62 + 6)(92 + 6)(202 + 6).
The 4-by-4 magic squares consisting of different squares with constant 1218:
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Page of Squares : First Upload January 16, 2007 ; Last Revised January 16, 2014
by Yoshio Mimura, Kobe, Japan
1220
1220 = (12 + 22 + 32 + ... + 3042) / (12 + 22 + 32 + ... + 282).
Page of Squares : First Upload November 25, 2008 ; Last Revised November 25, 2008by Yoshio Mimura, Kobe, Japan
1221
12212 = 93 + 443 + 1123.
6k + 408k + 690k + 921k are squares for k = 1,2,3 (452, 12212, 343172).
The 4-by-4 magic squares consisting of different squares with constant 1221:
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Page of Squares : First Upload June 30, 2008 ; Last Revised April 15, 2011
by Yoshio Mimura, Kobe, Japan
1224
12242 = 43 + 723 + 1043.
12242 = (1 + 2)(3)(4)(5 + 6 + 7)(8)(9 + 10 + ... + 25).
12242 = (12 + 8)(32 + 8)(42 + 8)(202 + 8) = (12 + 8)(82 + 8)(482 + 8).
Page of Squares : First Upload January 16, 2007 ; Last Revised December 14, 2013by Yoshio Mimura, Kobe, Japan
1225
the square of 35.
12252 = 703 + 1053 = 73 + 513 + 1113.
12252 = (12 + 6)(4632 + 6).
Komachi equations:
12252 = 94 * 84 * 74 * 64 * 54 / 4324 */ 14.
12252 = (1)(2 + 3)(4 + 5 + ... + 10)(11 + 12 + ... + 24)(25).
12252 = 13 + 23 + ... + 493.
Page of Squares : First Upload January 16, 2007 ; Last Revised December 14, 2013by Yoshio Mimura, Kobe, Japan
1226
12262 = 1503076, a zigzag square.
26k + 338k + 910k + 1226k are squares for k = 1,2,3 (502, 15642, 513322).
Page of Squares : First Upload January 16, 2007 ; Last Revised April 15, 2011by Yoshio Mimura, Kobe, Japan
1227
The 4-by-4 magic square consisting of different squares with constant 1227:
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Page of Squares : First Upload January 16, 2007 ; Last Revised January 6, 2010
by Yoshio Mimura, Kobe, Japan
1228
12282 = 1507984, a square with different digits.
Page of Squares : First Upload January 16, 2007 ; Last Revised January 16, 2007by Yoshio Mimura, Kobe, Japan
1230
12302 = (12 + 9)(142 + 9)(272 + 9) = (52 + 5)(62 + 5)(352 + 5).
66k + 210k + 1230k + 1410k are squares for k = 1,2,3 (542, 18842, 683642).
The 4-by-4 magic squares consisting of different squares with constant 1230:
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Page of Squares : First Upload January 6, 2010 ; Last Revised December 14, 2013
by Yoshio Mimura, Kobe, Japan
1231
12312 = 1515361, a zigzag square.
Page of Squares : First Upload January 16, 2007 ; Last Revised January 16, 2007by Yoshio Mimura, Kobe, Japan
1232
12322 = 73 + 333 + 1143.
385k + 1232k + 2156k + 2156k are squares for k = 1,2,3 (772, 33112, 1482252).
Page of Squares : First Upload June 30, 2008 ; Last Revised April 15, 2011by Yoshio Mimura, Kobe, Japan
1233
12332± 2 are primes.
1233 = 122 + 332.
1233 = 122 + 332.
1233k + 27948k + 55074k + 84666k are squares for k = 1,2,3 (4112, 1048052, 282098072).
12332 = 163 + 573 + 1103 = 64 + 64 + 244 + 334.
Page of Squares : First Upload January 16, 2007 ; Last Revised December 29, 2013by Yoshio Mimura, Kobe, Japan
1234
12342 = 1522756, 12 + 52 + 22 + 22 + 72 + 52 + 62 = 122.
12342 = 403 + 453 + 1113.
Page of Squares : First Upload January 16, 2007 ; Last Revised June 30, 2008by Yoshio Mimura, Kobe, Japan
1235
12352 = 1525225, a square with 3 kinds of digits 1,2 and 5.
12352 = 1525225 , 1 * 5 * 252 - 25 = 1235.
72865k + 167960k + 232180k + 1052220k are squares for k = 1,2,3 (12352, 10929752, 10874854252).
Page of Squares : First Upload January 16, 2007 ; Last Revised April 15, 2011by Yoshio Mimura, Kobe, Japan
1236
12362 = 1527696, a zigzag square.
Page of Squares : First Upload January 16, 2007 ; Last Revised January 16, 2007by Yoshio Mimura, Kobe, Japan
1239
1 / 1239 = 0.00080710250201..., 82 + 02 + 72 + 102 + 252 + 02 + 202 + 12 = 1239,
1 / 1239 = 0.00080710250201..., 82 + 02 + 72 + 102 + 252 + 0202 + 12 = 1239,
1 / 1239 = 0.00080710250201..., 82 + 072 + 102 + 252 + 02 + 202 + 12 = 1239,
1 / 1239 = 0.00080710250201..., 82 + 072 + 102 + 252 + 0202 + 12 = 1239.
12392 = 1535121, a zigzag square.
12392± 2 are primes.
(12392 - 5) = (32 - 5)(42 - 5)(122 - 5)(162 - 5).
The 4-by-4 magic squares consisting of different squares with constant 1239:
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Page of Squares : First Upload January 16, 2007 ; Last Revised December 29, 2013
by Yoshio Mimura, Kobe, Japan
1241
12412 = 1453 - 1443 + 1433 - 1423 + ... + 13.
12 + 22 + 32 + 42 + ... + 12412 = 637850421 consisting of different digits (the first 9-digit sum, there are 2 such sums).
12412 = 672 + 692 + 712 + 732 + 742 + 752 + 762 + ... + 2112.
Page of Squares : First Upload January 16, 2007 ; Last Revised January 22, 2007by Yoshio Mimura, Kobe, Japan
1242
1242 = (12 + 22 + 32 + ... + 802) / (12 + 22 + 32 + ... + 72).
12422 = (1)(2 + 3 + ... + 7)(8 + 9 + ... + 15)(16 + 17 + ... + 38).
12422 = (12 + 5)(22 + 5)(1692 + 5) = (12 + 5)(82 + 5)(612 + 5) = (72 + 5)(1692 + 5).
12422 = (50 + 51+ 52)2 + (53 + 54 + 55)2 + (56 + 57 + 58)2 + ... + (116 + 117 + 118)2.
The 4-by-4 magic squares consisting of different squares with constant 1242:
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Page of Squares : First Upload January 16, 2007 ; Last Revised December 14, 2013
by Yoshio Mimura, Kobe, Japan
1243
12432 = (74 + 75)2 + (76 + 77)2 + (78 + 79)2 + ... + (138 + 139)2.
222497k + 420134k + 422620k + 479798k are squares for k = 1,2,3 (12432, 7967632, 5206815132).
39776k + 124300k + 381601k + 999372k are squares for k = 1,2,3 (12432, 10776812, 10274575852).
by Yoshio Mimura, Kobe, Japan
1245
12452 = 1550025, 1 * 5 * 500 / 2 - 5 = 1245.
The 4-by-4 magic squares consisting of different squares with constant 1245:
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Page of Squares : First Upload January 16, 2007 ; Last Revised January 6, 2010
by Yoshio Mimura, Kobe, Japan
1246
12462 = 1552516, 1552 - 51 * 6 = 1246.
12462 = (32 + 5)(3332 + 5).
Page of Squares : First Upload January 16, 2007 ; Last Revised December 14, 2013by Yoshio Mimura, Kobe, Japan
1247
12475 = 3015312078631007 :
302 + 12 + 52 + 32 + 12 + 22 + 02 + 72 + 82 + 62 + 32 + 102 + 02 + 72 = 1247.
by Yoshio Mimura, Kobe, Japan
1248
12482± 5 are primes.
12482 = (1)(2 + 3 + ... + 14)(15 + 16 + 17)(18 + 19 + ... + 30).
12482 = (23 + 8)(463 + 8).
Page of Squares : First Upload January 16, 2007 ; Last Revised January 16, 2014by Yoshio Mimura, Kobe, Japan
1250
12502 = 1562500, 1 = 12, 562500 = 7502.
12502 = 1562500, 1 / 5 * 6250 + 0 = 1250.
12502 = 493 + 783 + 993 = 254 + 254 + 254 + 254 = 58 + 58 + 58 + 58.
12502 = (1)(2)(3 + 4 + 5 + 6 + 7)(8 + 9 + 10 + 11 + 12)(13 + 14 + ... + 37).
12502 = (12 + 9)(42 + 9)(792 + 9).
Page of Squares : First Upload January 16, 2007 ; Last Revised December 14, 2013by Yoshio Mimura, Kobe, Japan
1251
12512 = 1565001, 15 / 6 * 500 + 1 = 1251.
The 4-by-4 magic square consisting of different squares with constant 1251:
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Page of Squares : First Upload January 16, 2007 ; Last Revised January 12, 2010
by Yoshio Mimura, Kobe, Japan
1252
12522 = 343 + 363 + 1143.
Page of Squares : First Upload June 30, 2008 ; Last Revised June 30, 2008by Yoshio Mimura, Kobe, Japan
1253
85204k + 370888k + 526260k + 587657k are squares for k = 1,2,3 (12532, 8758472, 6327136272).
Page of Squares : First Upload April 15, 2011 ; Last Revised April 15, 2011by Yoshio Mimura, Kobe, Japan
1254
12542± 5 are primes.
12542 = 93 + 833 + 1003.
12542 = (22 + 2)(32 + 2)(62 + 2)(252 + 2) = (22 + 2)(82 + 2)(632 + 2) = (62 + 2)(82 + 2)(252 + 2).
The 4-by-4 magic squares consisting of different squares with constant 1254:
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The 5-by-5 magic square consisting of different squares with constant 1254:
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Page of Squares : First Upload June 30, 2008 ; Last Revised January 16, 2014
by Yoshio Mimura, Kobe, Japan
1256
12562 = 1577536, a square with odd digits except the last digit 6.
12562± 3 are primes.
Page of Squares : First Upload August 24, 2013 ; Last Revised August 24, 2013by Yoshio Mimura, Kobe, Japan
1257
12572 = 24 + 24 + 274 + 324.
12572 = 1580049 appears in the decimal expressions of e:
e = 2.71828•••1580049••• (from the 90583rd digit)
by Yoshio Mimura, Kobe, Japan
1258
Komachi equation: 12582 = 9872 + 652 * 42 * 32 - 22 - 12.
Page of Squares : First Upload July 20, 2010 ; Last Revised July 20, 2010by Yoshio Mimura, Kobe, Japan
1260
12602 = (12 + 5)(32 + 5)(52 + 5)(252 + 5) = (42 - 1)(62 - 1)(552 - 1) = (42 - 1)(62 - 1)(72 - 1)(82-1)
= (42 - 1)(82 - 1)(412 - 1).
12602 = (1)(2)(3)(4)(5)(6 + 7 + 8)(9 + 10 + ... + 36),
12602 = (1)(2)(3)(4 + 5)(6 + 7 + 8 + 9)(10)(11 + 12 + ... + 17),
12602 = (1)(2)(3)(4 + 5 + ... + 17)(18 + 19 + ... + 62),
12602 = (1)(2)(3)(4 + 5 + ... + 8)(9)(10)(11 + 12 + ... + 17),
12602 = (1)(2)(3)(4 + 5 + 6)(7)(8)(9 + 10 + ... + 26),
12602 = (1)(2)(3)(4 + 5 + 6)(7 + 8 + 9)(10 + 11 + ... + 39),
12602 = (1)(2)(3 + 4)(5 + 6 + ... + 19)(20 + 21 + ... + 40),
12602 = (1)(2)(3 + 4)(5 + 6 + 7)(8 + 9 + ... + 112),
12602 = (1)(2)(3 + 4 + ... + 11)(12)(13 + 14 + ... + 47),
12602 = (1)(2)(3 + 4 + ... + 11)(12 + 13)(14 + 15 + ... + 34),
12602 = (1)(2)(3 + 4 + ... + 17)(18)(19 + 20 + ... + 30),
12602 = (1)(2)(3 + 4 + 5 + 6)(7)(8 + 9 + ... + 112),
12602 = (1)(2)(3 + 4 + 5 + 6)(7 + 8 + ... + 14)(15 + 16 + ... + 35),
12602 = (1)(2)(3 + 4 + 5 + 6)(7 + 8 + ... + 18)(19 + 20 + ... + 30),
12602 = (1)(2)(3 + 4 + 5 + 6 + 7)(8)(9 + 10 + ... + 89),
12602 = (1)(2)(3 + 4 + 5 + 6 + 7)(8 + 9 + ... + 13)(14 + 15 + ... + 34),
12602 = (1)(2)(3 + 4 + ... + 9)(10 + 11)(12)(13 + 14 + ... + 17),
12602 = (1)(2)(3 + 4 + 5)(6 + 7 + ... + 12)(13 + 14 + ... + 47),
12602 = (1)(2)(3 + 4 + 5)(6 + 7 + 8 + 9)(10 + 11)(12 + 13 + ... + 18),
12602 = (1)(2)(3 + 4 + 5)(6 + 7 + 8)(9 + 10 + 11 + 12)(13 + 14 + 15 + 16 + 17),
12602 = (1)(2)(3 + 4 + 5)(6 + 7 + 8)(9 + 10 + 11)(12 + 13 + ... + 18),
12602 = (1)(2 + 3)(4)(5)(6)(7)(8 + 9 + ... + 28),
12602 = (1)(2 + 3)(4)(5 + 6 + ... + 10)(11 + 12 + ... + 17)(18),
12602 = (1)(2 + 3 + ... + 13)(14 + 15 + ... + 34)(35),
12602 = (1)(2 + 3 + ... + 13)(14 + 15 + 16)(17 + 18 + ... + 32),
12602 = (1)(2 + 3 + ... + 19)(20)(21 + 22 + ... + 35),
12602 = (1)(2 + 3 + 4 + 5)(6 + 7 + ... + 10)(11 + 12 + ... + 16)(17 + 18),
12602 = (1)(2 + 3 + 4 + 5)(6 + 7 + 8)(9 + 10 + ... + 16)(17 + 18 + 19),
12602 = (1)(2 + 3 + 4 + 5 + 6)(7 + 8 + ... + 11)(12 + 13 + ... + 60),
12602 = (1)(2 + 3 + ... + 6)(7 + 8 + ... + 13)(14 + 15 + ... + 49),
12602 = (1)(2 + 3 + ... + 6)(7 + 8 + ... + 20)(21 + 22 + ... + 35),
12602 = (1)(2 + 3 + ... + 6)(7 + 8 + ... + 398),
12602 = (1)(2 + 3 + ... + 7)(8)(9 + 10 + ... + 12)(13 + 14 + ... + 22),
12602 = (1)(2 + 3 + ... + 8)(9)(10)(11 + 12 + 13)(14),
12602 = (1)(2 + 3 + ... + 8)(9 + 10 + ... + 23)(24 + 25 + ... + 30),
12602 = (1)(2 + 3 + 4)(5 + 6 + ... + 9)(10)(11 + 12 + 13)(14),
12602 = (1)(2 + 3 + 4)(5 + 6 + 7)(8 + 9 + ... + 27)(28),
12602 = (1 + 2)(3)(4)(5 + 6 + ... + 10)(11 + 12 + ... + 45),
12602 = (1 + 2)(3)(4)(5 + 6 + ... + 19)(20 + 21 + ... + 29),
12602 = (1 + 2)(3)(4)(5 + 6 + ... + 25)(26 + 27 + ... + 30),
12602 = (1 + 2)(3)(4)(5 + 6 + ... + 44)(45),
12602 = (1 + 2)(3)(4 + 5 + ... + 10)(11 + 12 + ... + 85),
12602 = (1 + 2)(3)(4 + 5 + ... + 8)(9 + 10 + ... + 15)(16 + 17 + ... + 19),
12602 = (1 + 2)(3)(4 + 5 + 6)(7 + 8)(9 + 10 + ... + 40),
12602 = (1 + 2)(3)(4 + 5 + 6)(7 + 8 + ... + 153),
12602 = (1 + 2)(3 + 4)(5 + 6 + ... + 19)(20)(21),
12602 = (1 + 2)(3 + 4)(5 + 6 + 7)(8)(9 + 10 + ... + 33),
12602 = (1 + 2)(3 + 4 + ... + 12)(13 + 14 + ... + 19)(20 + 21 + 22),
12602 = (1 + 2)(3 + 4 + ... + 18)(19 + 20 + ... + 81),
12602 = (1 + 2)(3 + 4 + ... + 6)(7)(8)(9 + 10 + ... + 33),
12602 = (1 + 2)(3 + 4 + ... + 9)(10 + 11)(12 + 13 + ... + 36),
12602 = (1 + 2)(3 + 4 + 5)(6 + 7 + ... + 14)(15 + 16 + ... + 34),
12602 = (1 + 2)(3 + 4 + 5)(6 + 7 + ... + 9)(10 + 11)(12 + 13 + ... + 16),
12602 = (1 + 2)(3 + 4 + 5)(6 + 7 + 8)(9 + 10 + 11)(12 + 13 + ... + 16),
12602 = (1 + 2 + ... + 14)(15)(16 + 17 + ... + 47),
12602 = (1 + 2 + ... + 14)(15 + 16 + ... + 174),
12602 = (1 + 2 + ... + 14)(15 + 16 + ... + 21)(22 + 23 + ... + 26),
12602 = (1 + 2 + ... + 4)(5)(6 + 7 + ... + 21)(22 + 23 + ... + 27),
12602 = (1 + 2 + ... + 4)(5 + 6 + 7)(8 + 9 + ... + 13)(14 + 15 + ... + 21),
12602 = (1 + 2 + ... + 5)(6)(7)(8)(9 + 10 + ... + 26),
12602 = (1 + 2 + ... + 5)(6)(7 + 8 + 9)(10 + 11 + ... + 39),
12602 = (1 + 2 + ... + 5)(6 + 7 + ... + 10)(11 + 12 + ... + 73),
12602 = (1 + 2 + ... + 5)(6 + 7 + ... + 15)(16 + 17 + ... + 47),
12602 = (1 + 2 + ... + 5)(6 + 7 + ... + 26)(27 + 28 + ... + 36),
12602 = (1 + 2 + ... + 8)(9 + 10 + ... + 12)(13 + 14 + ... + 47),
12602 = (1 + 2 + 3)(4)(5)(6 + 7 + 8)(9 + 10 + ... + 36),
12602 = (1 + 2 + 3)(4 + 5)(6 + 7 + ... + 9)(10)(11 + 12 + ... + 17),
12602 = (1 + 2 + 3)(4 + 5 + ... + 17)(18 + 19 + ... + 62),
12602 = (1 + 2 + 3)(4 + 5 + ... + 8)(9)(10)(11 + 12 + ... + 17),
12602 = (1 + 2 + 3)(4 + 5 + 6)(7)(8)(9 + 10 + ... + 26),
12602 = (1 + 2 + 3)(4 + 5 + 6)(7 + 8 + 9)(10 + 11 + ... + 39).
by Yoshio Mimura, Kobe, Japan
1261
12612 = 573 + 1123.
Page of Squares : First Upload June 30, 2008 ; Last Revised June 30, 2008by Yoshio Mimura, Kobe, Japan
1262
12622 = Sum (19x + 3)2 (x=0,1,...,23).
Page of Squares : First Upload January 16, 2007 ; Last Revised January 16, 2007by Yoshio Mimura, Kobe, Japan
1263
The 4-by-4 magic square consisting of different squares with constant 1263:
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Page of Squares : First Upload January 12, 2010 ; Last Revised January 12, 2010
by Yoshio Mimura, Kobe, Japan
1264
12642± 3 are primes.
Page of Squares : First Upload January 13, 2014 ; Last Revised January 13, 2014by Yoshio Mimura, Kobe, Japan
1265
1265k + 7084k + 16192k + 39468k are squares for k = 1,2,3 (2532, 432632, 81291432).
1265k + 1529k + 3817k + 5489k are squares for k = 1,2,3 (1102, 69742, 4760142).
12652 = 1600225, 1600 = 402, 225 = 152.
12652 = 1600225, 16 = 42 and 225 = 152.
Page of Squares : First Upload January 16, 2007 ; Last Revised April 15, 2011by Yoshio Mimura, Kobe, Japan
1266
12662± 5 are primes.
The 4-by-4 magic squares consisting of different squares with constant 1266:
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Page of Squares : First Upload January 12, 2010 ; Last Revised January 16, 2014
by Yoshio Mimura, Kobe, Japan
1267
12672 = 1605289, a square with different digits.
12672 = 1605289, 1 + 6 + 0 + 5 * 28 * 9 = 1267.
217924k + 225526k + 470057k + 691782k are squares for k = 1,2,3 (12672, 8932352, 6758266692).
12672 = 95 + 125 + 125 + 165.
Page of Squares : First Upload January 16, 2007 ; Last Revised April 15, 2011by Yoshio Mimura, Kobe, Japan
1268
12682 = 1607824, a square with different digits.
Loop of length 10 by the function f(N) = ... + c2 + b2 + a2 where N = ... + 1002c + 100b + a:
1268 - 4768 - 6833 - 5713 - 3418 - 1480 - 6596 - 13441 - 2838 - 2228 - 1268
(Note f(1268) = 122 + 682 = 4768, f(4768) = 472 + 682 = 6833, etc. See 41)
Komachi equation: 12682 = 987 * 6 * 543 / 2 + 1.
Page of Squares : First Upload January 16, 2007 ; Last Revised January 18, 2010by Yoshio Mimura, Kobe, Japan
1269
A cubic polynomial:
(X + 8962)(X + 12692)(X + 22682) = X3 + 27492X2 + 37021322X + 25787704322.
Komachi equation: 12692 = 9872 / 62 * 542 * 32 / 212.
The 4-by-4 magic squares consisting of different squares with constant 1269:
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Page of Squares : First Upload January 16, 2007 ; Last Revised July 20, 2010
by Yoshio Mimura, Kobe, Japan
1273
Cubic polynomials:
(X + 2642)(X + 8642)(X + 12732) = X3 + 15612X2 + 11724722X + 2903662082,
(X + 5762)(X + 6882)(X + 9032) = X3 + 12732X2 + 9019682X + 3578480642.
12732 = 44 + 84 + 234 + 344.
Page of Squares : First Upload January 16, 2007 ; Last Revised June 30, 2008by Yoshio Mimura, Kobe, Japan
1274
1 / 1274 = 0.000784..., 784 = 282.
12742 = 1623076, a zigzag square.
12742 = 1623076 , 16 - 2 + 30 * 7 * 6 = 1274.
Komachi equation: 12742 = 12 * 2342 * 562 * 72 / 82 / 92.
938k + 1274k + 3430k + 6902k are squares for k = 1,2,3 (1122, 78682, 6099522).
14k + 1162k + 1274k + 2450k are squares for k = 1,2,3 (702, 29962, 1354362).
490k + 1022k + 1274k + 6818k are squares for k = 1,2,3 (982, 70282, 5658522).
The 4-by-4 magic squares consisting of different squares with constant 1274:
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Page of Squares : First Upload January 16, 2007 ; Last Revised April 15, 2011
by Yoshio Mimura, Kobe, Japan
1275
1 / 1275 = 0.000784..., 784 = 282.
Komachi equation: 12752 = 92 * 82 * 7652 / 4322 * 102.
12752 = (1)(2 + 3)(4 + 5 + ... + 13)(14 + 15 + ... + 88).
12752 = (13 + 23 + ... + 503).
12752 = 93 + 403 + 1163 = 503 + 703 + 1053.
12752 + 12762 + 12772 + ... + 13002 = 13012 + 13022 + 13032 + ... + 13252.
The 4-by-4 magic square consisting of different squares with constant 1275:
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Page of Squares : First Upload January 16, 2007 ; Last Revised September 9, 2011
by Yoshio Mimura, Kobe, Japan
1276
12762 = 1628176, a zigzag square.
1276k + 1529k + 1738k + 5258k are squares for k = 1,2,3 (992, 58852, 3953072).
Page of Squares : First Upload January 16, 2007 ; Last Revised April 15, 2011by Yoshio Mimura, Kobe, Japan
1277
12772 = 1630729, a square with different digits.
(12772 - 9) = (42 - 9)(52 - 9)(102 - 9)(132 - 9).
12772 = 1630729 appears in the decimal expressions of e:
e = 2.71828•••1630729••• (from the 139786th digit)
by Yoshio Mimura, Kobe, Japan
1278
12782 = 1633284, 1 * 633 * 2 + 8 + 4 = 1278.
12782 = 34 + 74 + 294 + 314.
The 4-by-4 magic squares consisting of different squares with constant 1278:
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Page of Squares : First Upload January 16, 2007 ; Last Revised January 12, 2010
by Yoshio Mimura, Kobe, Japan
1281
12812 = 502 + 512 + 522 + 532 + 542 + 552 + 562 + ... + 1712.
The 4-by-4 magic squares consisting of different squares with constant 1281:
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Page of Squares : First Upload January 22, 2007 ; Last Revised January 12, 2010
by Yoshio Mimura, Kobe, Japan
1282
12822 = 1643524, 1 * 6 * 43 * 5 - 2 * 4 = 1282.
Komachi equation: 12822 = 92 * 82 - 72 - 62 + 52 + 42 * 322 * 102.
Page of Squares : First Upload January 16, 2007 ; Last Revised July 20, 2010by Yoshio Mimura, Kobe, Japan
1286
12862 = 403 + 413 + 1153.
Page of Squares : First Upload June 30, 2008 ; Last Revised June 30, 2008by Yoshio Mimura, Kobe, Japan
1287
12872 = 1656369, a square pegged by 6.
12872 = 1656369, 1656 - 369 = 1287.
(12 + 22 + ... + 12872) = (12 + 22)(12 + 22 + ... +102)(12 + 22 + ... + 1032).
12872 = 43 + 813 + 1043.
12872 = (1)(2 + 3 + 4)(5 + 6)(7 + 8 + ... + 32)(33).
12872 = (20 + 21 + 22)2 + (23 + 24 + 25)2 + (26 + 27 + 28)2 + ... + (116 + 117 + 118)2,
12872 = (113 + 114 + 115)2 + (116 + 117 + 118)2 + (119 + 120 + 121)2 + ... + (143 + 144 + 145)2.
The 4-by-4 magic square consisting of different squares with constant 1287:
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Page of Squares : First Upload January 16, 2007 ; Last Revised January 12, 2010
by Yoshio Mimura, Kobe, Japan
1288
12882 = 1658944, 165 * 8 - 9 * 4 + 4 = 1288.
294k + 1288k + 1617k + 2730k are squares for k = 1,2,3 (772, 34372, 1635132).
Page of Squares : First Upload January 16, 2007 ; Last Revised April 15, 2011by Yoshio Mimura, Kobe, Japan
1290
Komachi equations:
12902 = 92 + 82 - 72 + 62 * 52 * 432 + 22 - 102 = - 92 - 82 + 72 + 62 * 52 * 432 - 22 + 102.
The 4-by-4 magic squares consisting of different squares with constant 1290:
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Page of Squares : First Upload January 12, 2010 ; Last Revised July 20, 2010
by Yoshio Mimura, Kobe, Japan
1291
12912 = 1666681, a square with 3 kinds of digits 1, 6 and 8.
Page of Squares : First Upload January 16, 2007 ; Last Revised January 16, 2007by Yoshio Mimura, Kobe, Japan
1292
513k + 1292k + 3382k + 3838k are squares for k = 1,2,3 (952, 53012, 3122652).
Page of Squares : First Upload April 15, 2011 ; Last Revised April 15, 2011by Yoshio Mimura, Kobe, Japan
1293
1 / 1293 = 0.000773395..., 72 + 72 + 332 + 92 + 52 = 1293.
Page of Squares : First Upload January 16, 2007 ; Last Revised January 16, 2007by Yoshio Mimura, Kobe, Japan
1295
139860k + 195545k + 562030k + 779590k are squares for k = 1,2,3 (12952, 9906752, 8133571252).
Page of Squares : First Upload April 15, 2011 ; Last Revised April 15, 2011by Yoshio Mimura, Kobe, Japan
1296
the square of 36.
1296 = (1 + 29 + 6)2.
12962 = 1679616, 1 + 679 + 616 = 1296.
1296 = (12 + 8)(42 + 8)(82 + 8)(102 + 8) = (22 + 8)(82 + 8)(442 + 8).
Komachi equations:
12962 = 122 * 32 * 42 * 562 / 72 / 82 * 92 = 122 * 32 * 42 / 562 * 72 * 82 * 92.
12962 = 363 + 723 + 1083 = 67 + 67 + 67 + 67 + 67 + 67.
12962 = (1)(2)(3)(4)(5 + 6 + 7)(8 + 9 + ... + 88).
12962 = (1)(2)(3 + 4 + ... + 6)(7 + 8 + 9)(10 + 11 + ... + 17)(18),
12962 = (18)(28)(38),
12962 = (1 + 2)(3 + 4 + ... + 6)(7 + 8 + ... + 249),
12962 = (1 + 2 + 3)(4)(5 + 6 + 7)(8 + 9 + ... + 88).
12962 = (2 + 3 + 4 + ... + 10)2 + (11 + 12 + 13 + ... + 19)2 + (20 + 21 + 22 + ... + 28)2 + ... + (74 + 75 + 76 + ... + 82)2.
Page of Squares : First Upload January 16, 2007 ; Last Revised December 14, 2013by Yoshio Mimura, Kobe, Japan
1297
12972 = 14 + 64 + 64 + 364.
Page of Squares : First Upload June 30, 2008 ; Last Revised June 30, 2008by Yoshio Mimura, Kobe, Japan
1298
1298 = (12 + 22 + 32 + ... + 71392) / (12 + 22 + 32 + ... + 6542).
154k + 814k + 1298k + 2090k are squares for k = 1,2,3 (662, 25962, 1089002).
The 4-by-4 magic squares consisting of different squares with constant 1298:
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Page of Squares : First Upload November 25, 2008 ; Last Revised April 15, 2011
by Yoshio Mimura, Kobe, Japan
1299
87033k + 332544k + 475434k + 792390k are squares for k = 1,2,3 (12992, 9859412, 8015154752).
The 4-by-4 magic square consisting of different squares with constant 1299:
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Page of Squares : First Upload January 12, 2010 ; Last Revised April 15, 2011
by Yoshio Mimura, Kobe, Japan