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1200 - 1299

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).

Page of Squares : First Upload January 16, 2007 ; Last Revised January 16, 2007
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)

Page of Squares : First Upload January 16, 2007 ; Last Revised November 4, 2008
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, 2007
by Yoshio Mimura, Kobe, Japan

1203

12032 = 63 + 163 + 1133 = 443 + 813 + 943.

Page of Squares : First Upload June 30, 2008 ; Last Revised June 30, 2008
by Yoshio Mimura, Kobe, Japan

1205

12052 = 13 + 613 + 1073.

Page of Squares : First Upload June 30, 2008 ; Last Revised June 30, 2008
by Yoshio Mimura, Kobe, Japan

1206

The 4-by-4 magic squares consisting of different squares with constant 1206:

02 12 72342
22312152 42
192122262 52
292102162 32
   
02 12 72342
62252232 42
212162222 52
272182122 32
   
02 12232262
62252172162
92242182152
332 22 82 72
   
02 22192292
62322112 52
212132202142
272 32182122
   
02 62 92332
132192242102
142282152 12
292 52182 42
02 62212272
92252202102
152232142162
302 42132112
     
12 92102322
162142272 52
182202192112
252232 42 62
     
12102232242
162272142 52
182192202112
252 42 92222
     
32112202262
122222232 72
182242 92152
272 52142162

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)

Page of Squares : First Upload November 4, 2008 ; Last Revised April 15, 2011
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:

02 22 72342
82252222 62
192162242 42
282182102 12
     
02 42132322
142302 82 72
222172202 62
232 22242102
     
02132162282
142202182172
222 82252 62
232242 22102

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, 2008
by 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, 2007
by 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, 2014
by 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, 2010
by 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:

02 42192292
82322 72 92
232 32222142
252132182102
     
02 42192292
82322 72 92
232 32222142
252132182102
     
02 42192292
82322 72 92
232132182142
252 32222102
     
02 42192292
82322 92 72
232 32262 22
252132102182
02 52132322
112302142 12
162172232122
292 22182 72
     
02 82232252
112172182222
162282132 32
292 92142102
     
02 82232252
112172222182
162282 32132
292 92142102
     
12 22222272
42332 72 82
242 52192162
252102182132
12 22222272
72262182132
122232172162
322 32112 82
     
12 52 62342
122202252 72
172272142 22
282 82192 32
     
12102212262
122252202 72
172182112222
282132162 32
     
12102212262
122252202 72
172222112182
282 32162132
22 32232262
52162242192
172282 82 92
302132 72102
     
22 52102332
172282 92 82
212202192 42
222 32262 72
     
32 52202282
72312 82122
222 62232132
262142152112
     
32 72222262
82202232152
192252 62142
282122132112

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, 2008
by 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:

02 82142312
162 72302 42
172282 22122
262182112102
     
12 82162302
122282172 22
202 72242142
262182102112

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, 2013
by 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, 2013
by 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, 2011
by Yoshio Mimura, Kobe, Japan

1227

The 4-by-4 magic square consisting of different squares with constant 1227:

12 42112332
162292 92 72
212192202 52
232 32252 82

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, 2007
by 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:

02 52 72342
102252212 82
132242222 12
312 22162 32
     
12 32142322
132312 82 62
222162212 72
242 22232112
     
12102202272
112322 62 72
182 52252162
282 92132142

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, 2007
by 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, 2011
by 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, 2013
by 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, 2008
by 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, 2011
by Yoshio Mimura, Kobe, Japan

1236

12362 = 1527696, a zigzag square.

Page of Squares : First Upload January 16, 2007 ; Last Revised January 16, 2007
by 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:

12 52222272
92262192112
142232152172
312 32132102
     
12 62192292
112252222 32
212232132102
262 72152172

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, 2007
by 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:

02 32122332
52262212102
162192242 72
312142 92 22
     
02 72132322
152302 62 92
212 22262112
242172192 42
     
02132172282
152 62302 92
212262 22112
242192 72162

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).

Page of Squares : First Upload January 16, 2007 ; Last Revised April 15, 2011
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:

52 62202282
82222242112
162262132122
302 72102142
     
52 82162302
122112282142
202242132102
262222 62 72

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, 2013
by Yoshio Mimura, Kobe, Japan

1247

12475 = 3015312078631007 :
302 + 12 + 52 + 32 + 12 + 22 + 02 + 72 + 82 + 62 + 32 + 102 + 02 + 72 = 1247.

Page of Squares : First Upload December 8, 2008 ; Last Revised December 8, 2008
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, 2014
by 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, 2013
by 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:

02 72192292
92322 52112
212 32242152
272132172 82

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, 2008
by 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, 2011
by 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:

12 22152322
42212262112
92282172102
342 52 82 32
     
22 32202292
72322 92102
242 52222132
252142172122
     
22 52212282
82272192102
152222162172
312 42142 92
     
42 52222272
72182252162
172282 92102
302112 82132
42 62192292
72232242102
172252142122
302 82112132
     
62112162292
172142252122
202192182132
232242 72102

The 5-by-5 magic square consisting of different squares with constant 1254:

02 42152222232
82282 12182 92
112212162 62202
132 22242192122
302 32142 72102

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, 2013
by 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)

Page of Squares : First Upload June 30, 2008 ; Last Revised November 4, 2008
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, 2010
by 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).

Page of Squares : First Upload January 16, 2007 ; Last Revised December 14, 2013
by Yoshio Mimura, Kobe, Japan

1261

12612 = 573 + 1123.

Page of Squares : First Upload June 30, 2008 ; Last Revised June 30, 2008
by 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, 2007
by Yoshio Mimura, Kobe, Japan

1263

The 4-by-4 magic square consisting of different squares with constant 1263:

12 22132332
142312 92 52
212172222 72
252 32232102

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, 2014
by 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, 2011
by Yoshio Mimura, Kobe, Japan

1266

12662± 5 are primes.

The 4-by-4 magic squares consisting of different squares with constant 1266:

02 42 52352
112252222 62
192152262 22
282202 92 12
     
02 42172312
82322132 32
192152222142
292 12182102
     
12 32102342
152292142 22
162202232 92
282 42212 52
     
12 92202282
102262212 72
182222132172
292 52162122

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, 2011
by 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, 2010
by 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:

02 12222282
62262192142
122242182152
332 42102 82
     
02 62122332
162302 72 82
222 32262102
232182202 42
     
02 72 82342
122202252102
152282162 22
302 62182 32

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, 2008
by 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:

02 42232272
72332 62102
212 52222182
282122152112
     
02 72212282
122 12272202
172302 22 92
292182102 32

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:

02 52172312
112322 72 92
232 12242132
252152192 82

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, 2011
by 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)

Page of Squares : First Upload January 16, 2007 ; Last Revised November 4, 2008
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:

02 12112342
152302122 32
182192232 82
272 42222 72
     
02112142312
152302 32122
182 12282132
272162172 22
     
02132222252
152242212 62
182232 82192
272 22172162
     
12 32222282
52332 82102
242 62212152
262122172132
12 62202292
82332 52102
222 32232162
272122182 92
     
12 82222272
112262202 92
162232132182
302 32152122
     
22 42132332
52252222122
152212242 62
322142 72 32
     
22 42232272
92292162102
132152222202
322142 32 72
22 52152322
162252192 62
172122262132
272222 42 72
     
22 82112332
92272182122
132172282 62
322142 72 32
     
22 82112332
132172262122
232222162 32
242212152 62

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:

02 22112342
162 52302102
202262142 32
252242 82 42
     
02 22112342
162302102 52
202192222 62
252 42242 82
     
02132222252
152242212 62
182232 82192
272 22172162
     
22 32222282
42202242172
192262102122
302142112 82
22 32222282
52342 62 82
242 42202172
262102192122
     
22 32222282
62342 52 82
202 42242172
292102142122
     
22 42192302
52342 62 82
242102222112
262 32202142
     
22 52242262
82322 72122
222 62202192
272142162102

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, 2010
by Yoshio Mimura, Kobe, Japan

1286

12862 = 403 + 413 + 1153.

Page of Squares : First Upload June 30, 2008 ; Last Revised June 30, 2008
by 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:

12 52 62352
112262212 72
182152272 32
292192 92 22

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, 2011
by 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:

02 12 82352
72262232 62
202172242 52
292182112 22
     
12 22142332
32262222112
162212232 82
322132 92 42
     
12 22142332
32262222112
162232212 82
322 92132 42
     
12102172302
122312 42132
192 22272142
282152162 52
22 52192302
62252232102
172242162132
312 82122112
     
22 52192302
92322 82112
232 42242132
262152172102

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, 2007
by 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, 2011
by 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, 2007
by 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, 2011
by 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, 2013
by Yoshio Mimura, Kobe, Japan

1297

12972 = 14 + 64 + 64 + 364.

Page of Squares : First Upload June 30, 2008 ; Last Revised June 30, 2008
by 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:

02 42212292
132332 22 62
202122232152
272 72182142
     
02 72152322
92142302112
162272132122
312182 22 32

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:

12 42212292
72272202112
152232172162
322 52132 92

Page of Squares : First Upload January 12, 2010 ; Last Revised April 15, 2011
by Yoshio Mimura, Kobe, Japan