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1100 - 1199

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, 2011
by 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:

02 22162292
82302112 42
192142202122
262 12182102

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, 2014
by Yoshio Mimura, Kobe, Japan

1103

11032 = 1216609, a reversible square (9066121 = 30112).

Page of Squares : First Upload December 20, 2006 ; Last Revised December 20, 2006
by 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, 2006
by 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, 2013
by 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:

02 12232242
112302 62 72
162 32212202
272142102 92
     
22 62212252
72152242162
182262 52 92
272132 82122

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, 2006
by Yoshio Mimura, Kobe, Japan

1109

11092 = 1229881, 122 + 988 - 1 = 1109.

Page of Squares : First Upload December 20, 2006 ; Last Revised December 20, 2006
by 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:

02 12222252
72242172142
102232162152
312 22 92 82
     
02102132292
142282 32112
172 12262122
252152162 22
     
22 92202252
112222212 82
162232102152
272 42132142

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, 2013
by 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, 2007
by 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:

12 22182282
42242202112
142222172122
302 72102 82
     
22 72222242
102182172202
152262142 42
282 82122112

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, 2008
by Yoshio Mimura, Kobe, Japan

1119

The 4-by-4 magic squares consisting of different squares with constant 1119:

12 92142292
102232212 72
172222112152
272 52192 22
     
12 92192262
102232212 72
172222112152
272 52142132

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, 2010
by 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, 2006
by 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:

12 22212262
42252162152
92222192142
322 32 82 52
     
12 22212262
42312 82 92
232 62192142
242112162132
     
12 42 92322
142152262 52
212162192 82
222252 22 32
     
12 42122312
52242202112
142192232 62
302132 72 22
12 42122312
112242202 52
182132232102
262192 72 62
     
12 42122312
142292 72 62
212162202 52
222 32232102
     
12 92162282
112292 42122
182 22252132
262142152 52
     
42 82 92312
112152262102
122282132 52
292 72142 62

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.

Page of Squares : First Upload December 20, 2006 ; Last Revised December 20, 2006
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, 2008
by 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.)

Page of Squares : First Upload June 30, 2008 ; Last Revised November 4, 2008
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, 2008
by 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, 2006
by 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, 2006
by 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, 2014
by 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, 2011
by 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:

02 22132312
92192262 42
182252 82112
272122152 62
   
02 22132312
92292142 42
182 82252112
272152122 62
   
02 22172292
32252202102
152212182122
302 82112 72
   
02 22172292
92112262162
182282 52 12
272152122 62
   
02 32 62332
92142292 42
182232162 52
272202 12 22
02 32 62332
172102272 42
192252122 22
222202152 52
   
02 32 62332
172202212 22
192262 92 42
222 72242 52
   
02 32152302
92102282132
182252112 82
272202 22 12
   
02 92182272
172282 52 62
192102232122
222132162152
   
12 22202272
32242182152
102232192122
322 52 72 62
12 22202272
142252132122
192 82222152
242212 92 62
   
12 32102322
42302132 72
212 92242 62
262122172 52
   
12 32102322
62242212 92
162182232 52
292152 82 22
   
12 32102322
142 42292 92
192252122 22
242222 72 52
   
12 42212262
82252182112
132222152162
302 32122 92
12 52182282
62242212 92
162222152132
292 72122102
   
12 82132302
142292 42 92
192 22252122
242152182 32
   
22 52122312
82 72302112
212242 92 62
252222 32 42
   
22 82212252
112312 62 42
152 32242182
282102 92132
   
32 72202262
152272 62122
182162232 52
242102132172
32 82102312
92262162112
122152272 62
302132 72 42
     
32 92122302
152132262 82
182202172112
242222 52 72

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).

Page of Squares : First Upload December 20, 2006 ; Last Revised December 14, 2013
by Yoshio Mimura, Kobe, Japan

1135

11352 = 93 + 663 + 1003.

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

02 82172282
102302 42112
192 22242142
262132162 62

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).

Page of Squares : First Upload December 20, 2006 ; Last Revised October 4, 2011
by Yoshio Mimura, Kobe, Japan

1142

11422 = 1304164, a zigzag square.

Page of Squares : First Upload December 20, 2006 ; Last Revised December 20, 2006
by Yoshio Mimura, Kobe, Japan

1143

11432± 2 are primes.

Page of Squares : First Upload December 29, 2013 ; Last Revised December 29, 2013
by 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:

02 12112322
42252212 82
172182222 72
292142102 32
   
02 72162292
112302 52102
202 12242132
252142172 62
   
02 82112312
162282 52 92
192 32262102
232172182 22
   
12 42202272
62312 72102
222 52212142
252122162112
   
32 82172282
102292 62132
192 42252122
262152142 72

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.

Page of Squares : First Upload December 20, 2006 ; Last Revised December 20, 2006
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).

Page of Squares : First Upload April 12, 2011 ; Last Revised April 12, 2011
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, 2006
by 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)

Page of Squares : First Upload June 30, 2008 ; Last Revised January 6, 2011
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, 2006
by 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, 2013
by 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:

02 12232252
52282112152
132172212162
312 92 82 72
     
12 82192272
92252202 72
172212132162
282 52152112

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, 2013
by 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, 2014
by 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:

22 72 92322
122172252102
132282142 32
292 62162 52

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).

Page of Squares : First Upload December 14, 2013 ; Last Revised December 14, 2013
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:

02 22142312
122302 92 62
212162202 82
242 12222102
     
02122212242
142232202 62
172222 82182
262 22162152
     
22 72182282
92302 62122
202 42242132
262142152 82

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

1165

11652 = (12 + 4)(5212 + 4).

Page of Squares : First Upload December 14, 2013 ; Last Revised December 14, 2013
by 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:

22122172272
152292 62 82
192 92202182
242102212 72

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.)

Page of Squares : First Upload December 20, 2006 ; Last Revised August 24, 2013
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:

12 72212262
102252192 92
152222132172
292 32142112

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.

Page of Squares : First Upload December 20, 2006 ; Last Revised December 20, 2006
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, 2008
by 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:

12 82 92322
102252182112
132162272 42
302152 62 32
     
22 62132312
142302 52 72
212 32242122
232152202 42
     
22 62172292
102302 72112
212 32242122
252152162 82
     
32 42192282
62272182 92
152202172162
302 52142 72

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).

Page of Squares : First Upload December 20, 2006 ; Last Revised December 14, 2013
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, 2006
by 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:

02 42142312
102302132 22
172162222122
282 12182 82
     
02 72102322
172282 62 82
202 42262 92
222182192 22

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.

Page of Squares : First Upload December 20, 2006 ; Last Revised December 20, 2006
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, 2011
by 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, 2013
by 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).

Page of Squares : First Upload December 1, 2008 ; Last Revised April 12, 2011
by Yoshio Mimura, Kobe, Japan

1178

11782 = 194 + 214 + 274 + 274.

The 4-by-4 magic square consisting of different squares with constant 1178:

02 52 82332
92102312 62
162272122 72
292182 32 22

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:

02 32212272
72252192122
132232162152
312 42112 92

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, 2006
by 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, 2006
by 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:

02 52142312
132302 72 82
222 12242112
232162192 62
     
12 42182292
52262202 92
162212172142
302 72132182
     
22 72202272
92262192 82
162212142172
292 42152102

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, 2008
by 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, 2008
by Yoshio Mimura, Kobe, Japan

1185

The 4-by-4 magic square consisting of different squares with constant 1185:

02 12202282
52322102 62
222122192142
262 42182132

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, 2006
by 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).

Page of Squares : First Upload December 20, 2006 ; Last Revised December 14, 2013
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, 2011
by 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:

12 62 82332
172122262 92
182292 32 42
242132212 22
     
12 82152302
172262 92122
182212202 52
242 32222112
     
32 52162302
112272182 42
222202 92152
242 62232 72

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, 2013
by 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, 2006
by 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:

02 72112322
82252192122
132182262 52
312142 62 12
     
12 22102332
32262222 52
202172212 82
282152132 42
     
12 32202282
62262192112
142222172152
312 52122182
     
42 72202272
92222232102
162252122132
292 62112142

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, 2014
by 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:

02 42 52342
112162282 62
202272 82 22
262142182 12
   
02 42 52342
122212242 62
182262142 12
272 82202 22
   
02112202262
122 62242212
182282 52 82
272162142 42
   
02112202262
122242212 62
182222102172
272 42162142
   
42 82212262
112282162 62
222182102172
242 52202142

Page of Squares : First Upload December 20, 2006 ; Last Revised December 25, 2009
by Yoshio Mimura, Kobe, Japan