3200
32002 = 303 + 653 + 2153 = 803 + 1203 + 2003 = 404 + 404 + 404 + 404.
Page of Squares : First Upload August 10, 2008 ; Last Revised August 10, 2008by Yoshio Mimura, Kobe, Japan
3201
32012 = 10246401, 10 * 2 / 4 * 640 + 1 = 3201.
Page of Squares : First Upload June 11, 2007 ; Last Revised June 11, 2007by Yoshio Mimura, Kobe, Japan
3202
32022 = 10252804, 1 * 0 + 2 + 5 * 2 * 80 * 4 = 3202.
Page of Squares : First Upload June 11, 2007 ; Last Revised June 11, 2007by Yoshio Mimura, Kobe, Japan
3203
32032 = 10259209, 12 + 02 + 22 + 52 + 92 + 22 + 02 + 92 = 142.
Page of Squares : First Upload June 11, 2007 ; Last Revised June 11, 2007by Yoshio Mimura, Kobe, Japan
3204
32042 = (22 + 8)(92 + 8)(982 + 8).
32042 = 623 + 1293 + 1993.
Page of Squares : First Upload August 10, 2008 ; Last Revised December 21, 2013by Yoshio Mimura, Kobe, Japan
3206
32062 = 10278436, a square with different digits.
Page of Squares : First Upload June 11, 2007 ; Last Revised June 11, 2007by Yoshio Mimura, Kobe, Japan
3207
32072 = 10284849, 102 * 8 * 4 - 8 - 49 = 3207.
32072 = 164 + 184 + 234 + 564 = 164 + 384 + 414 + 484.
Page of Squares : First Upload June 11, 2007 ; Last Revised August 10, 2008by Yoshio Mimura, Kobe, Japan
3208
32082 = 24 + 344 + 464 + 464.
Page of Squares : First Upload August 10, 2008 ; Last Revised August 10, 2008by Yoshio Mimura, Kobe, Japan
3210
32102 = 353 + 1213 + 2043.
Page of Squares : First Upload August 10, 2008 ; Last Revised August 10, 2008by Yoshio Mimura, Kobe, Japan
3213
32132 = 1173 + 1473 + 1773.
Komachi equation: 32132 = 122 * 342 * 5672 / 82 / 92.
32132 = (74 + 75 + 76)2 + (77 + 78 + 79)2 + (80 + 81 + 82)2 + ... + (218 + 219 + 220)2.
Page of Squares : First Upload June 11, 2007 ; Last Revised October 1, 2010by Yoshio Mimura, Kobe, Japan
3214
32142 = 10329796, a zigzag square.
Page of Squares : First Upload June 11, 2007 ; Last Revised June 11, 2007by Yoshio Mimura, Kobe, Japan
3219
32192 = 13 + 123 + 2183 = 93 + 103 + 2183 = 1233 + 1373 + 1813.
Page of Squares : First Upload August 10, 2008 ; Last Revised August 10, 2008by Yoshio Mimura, Kobe, Japan
3220
32202 = 10368400, 10 / 3 * 6 + 8 * 400 = 3220.
Page of Squares : First Upload June 11, 2007 ; Last Revised June 11, 2007by Yoshio Mimura, Kobe, Japan
3221
32212 = 213 + 1473 + 1933.
Page of Squares : First Upload August 10, 2008 ; Last Revised August 10, 2008by Yoshio Mimura, Kobe, Japan
3224
32242 = (12 + 3)(72 + 3)(112 + 3)(202 + 3).
Page of Squares : First Upload December 21, 2013 ; Last Revised December 21, 2013by Yoshio Mimura, Kobe, Japan
3225
A cubic polynomial :
(X + 30962)(X + 32252)(X + 44802) = X3 + 63292X2 + 223789202X + 447310080002.
by Yoshio Mimura, Kobe, Japan
3226
32262 = 10407076, a zigzag square.
Page of Squares : First Upload June 11, 2007 ; Last Revised June 11, 2007by Yoshio Mimura, Kobe, Japan
3228
32282 = 10419984, 10 * 4 * 1 * 9 * 9 - 8 - 4 = 3228.
Page of Squares : First Upload June 11, 2007 ; Last Revised June 11, 2007by Yoshio Mimura, Kobe, Japan
3230
A 4x4 perfect magic square consisting of squares with the constant 3230.
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Page of Squares : First Upload June 11, 2007 ; Last Revised June 11, 2007
by Yoshio Mimura, Kobe, Japan
3231
32312 = 10439361, a zigzag square.
32312 = 10439361, 104 / 3 * 93 + 6 + 1 = 3231.
Page of Squares : First Upload June 11, 2007 ; Last Revised June 11, 2007by Yoshio Mimura, Kobe, Japan
3236
32365 = 354848165788722176 : 32 + 52 + 42 + 82 + 482 + 12 + 62 + 52 + 72 + 82 + 82 + 72 + 22 + 212 + 72 + 62 = 32 + 52 + 482 + 42 + 82 + 12 + 62 + 52 + 72 + 82 + 82 + 72 + 22 + 212 + 72 + 62 = 3236.
Page of Squares : First Upload December 8, 2008 ; Last Revised December 8, 2008by Yoshio Mimura, Kobe, Japan
3240
32402 = 363 + 723 + 2163.
32402 + 32412 + 32422 + ... + 32802 = 32812 + 32822 + 32832 + ... + 33202.
960k + 2080k + 2745k + 3240k are squares for k = 1,2,3 (952, 48252, 2541252).
Komachi equation: 32402 = 92 * 872 * 62 - 542 * 32 * 212.
Page of Squares : First Upload August 10, 2008 ; Last Revised September 13, 2011by Yoshio Mimura, Kobe, Japan
3241
32412 = 10504081, a zigzag square.
S2(3241) = S2(1126) + S2(3195), where S2(n) = 12 + 22 + 32 + 42 + ... + n2.
32412 = 10504081, 1 + 0 + 5 * 0 + 40 * 81 = 1 + 0 - 5 * 0 + 40 * 81 = 1 + 0 * 5 + 0 + 40 * 81
= 1 + 0 * 5 * 0 + 40 * 81 = 1 + 0 * 50 + 40 * 81 = 3241.
by Yoshio Mimura, Kobe, Japan
3245
32452 = 10530025, 12 + 02 + 52 + 32 + 02 + 02 + 22 + 52 = 82.
3245k + 7965k + 101185k + 235705k are squares for k = 1,2,3 (5902, 2566502, 1188761502).
517k + 869k + 3245k + 7469k are squares for k = 1,2,3 (1102, 82062, 6720342).
by Yoshio Mimura, Kobe, Japan
3246
32462 = 10536516, 10 * 5 * 3 + 6 * 516 = 3246.
Page of Squares : First Upload June 11, 2007 ; Last Revised June 11, 2007by Yoshio Mimura, Kobe, Japan
3247
32472 = 134 + 244 + 364 + 544.
Page of Squares : First Upload August 10, 2008 ; Last Revised August 10, 2008by Yoshio Mimura, Kobe, Japan
3248
32482± 3 are primes.
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
3249
The square of 57.
32492 = 573 + 1523 + 1903 = 1073 + 1633 + 1713.
3249 = 572, and 324 = 182, 9 = 32.
32495 = 362033331456891249 : 32 + 62 + 202 + 32 + 32 + 32 + 32 + 12 + 42 + 52 + 62 + 82 + 92 + 122 + 492 = 3249.
Page of Squares : First Upload June 11, 2007 ; Last Revised December 8, 2008by Yoshio Mimura, Kobe, Japan
3250
32502 = (12 + 1)(22 + 1)(182 + 1)(572 + 1) = (12 + 1)(22 + 1)(72 + 1)(82 + 1)(182 + 1)
= (22 + 1)(32 + 1)(82 + 1)(572 + 1) = (32 + 1)(182 + 1)(572 + 1)
= (32 + 1)(72 + 1)(82 + 1)(182 + 1) = (72 + 1)(82 + 1)(572 + 1) = (12 + 4)(32 + 4)(112 + 4)(362 + 4)
= (12 + 4)(42 + 4)(112 + 4)(292 + 4) = (22 + 9)(112 + 9)(792 + 9) = (412 + 9)(792 + 9).
1794k + 3250k + 12402k + 15678k are squares for k = 1,2,3 (1822, 203322, 24085882).
Page of Squares : First Upload May 27, 2011 ; Last Revised December 21, 2013by Yoshio Mimura, Kobe, Japan
3251
32512 = 10569001, 12 + 02 + 52 + 62 + 92 + 02 + 02 + 12 = 122.
Page of Squares : First Upload June 11, 2007 ; Last Revised June 11, 2007by Yoshio Mimura, Kobe, Japan
3254
32542 = 10588516, 1 + 0 - 5 + 8 * 8 * 51 - 6 = 3254.
Page of Squares : First Upload June 11, 2007 ; Last Revised June 11, 2007by Yoshio Mimura, Kobe, Japan
3255
32552 = (25 + 26 + 27 + 28 + 29 + 30)2 + (31 + 32 + 33 + 34 + 35 + 36)2 + (37 + 38 + 39 + 40 + 41 + 42)2 + ... + (169 + 170 +171 + 172 + 173 + 174)2.
32552 = (12 + 6)(32 + 6)(52 + 6)(572 + 6).
Page of Squares : First Upload June 11, 2007 ; Last Revised December 21, 2013by Yoshio Mimura, Kobe, Japan
3256
32562 = (12 + 7)(22 + 7)(172 + 7)(202 + 7) = (12 + 7)(202 + 7)(572 + 7)
= (22 + 7)(172 + 7)(572 + 7) = (92 + 7)(172 + 7)(202 + 7).
by Yoshio Mimura, Kobe, Japan
3258
Komachi eqations:
32582 = 92 + 82 - 72 + 62 * 5432 + 22 - 102 = - 92 - 82 + 72 + 62 * 5432 - 22 + 102.
by Yoshio Mimura, Kobe, Japan
3261
32612 = 10634121, a zigzag square.
Page of Squares : First Upload June 11, 2007 ; Last Revised June 11, 2007by Yoshio Mimura, Kobe, Japan
3262
32622 = 10640644, 12 + 02 + 62 + 42 + 02 + 62 + 42 + 42 = 112.
Page of Squares : First Upload June 11, 2007 ; Last Revised June 11, 2007by Yoshio Mimura, Kobe, Japan
3264
32642 = (32 - 1)(332 - 1)(352 - 1).
32642 = 403 + 803 + 2163 = 403 + 1523 + 1923.
Page of Squares : First Upload August 10, 2008 ; Last Revised December 21, 2013by Yoshio Mimura, Kobe, Japan
3267
32672 = 10673289, a square with different digits.
32672 = 12322 + 21232 + 21562 : 65122 + 32122 + 23212 = 76232.
32672 = 243 + 1533 + 1923 = 1083 + 1533 + 1803.
Page of Squares : First Upload June 11, 2007 ; Last Revised September 18, 2013by Yoshio Mimura, Kobe, Japan
3268
32682 = 10679824, a square with different digits.
32682 = 843 + 1543 + 1863 = 35 + 45 + 135 + 225 + 225.
Page of Squares : First Upload June 11, 2007 ; Last Revised August 10, 2008by Yoshio Mimura, Kobe, Japan
3270
32702 = (12 + 9)(102 + 9)(992 + 9).
Page of Squares : First Upload December 21, 2013 ; Last Revised December 21, 2013by Yoshio Mimura, Kobe, Japan
3274
32742 = 10719076, a zigzag square.
Page of Squares : First Upload June 11, 2007 ; Last Revised June 11, 2007by Yoshio Mimura, Kobe, Japan
3275
32752 = 1303 + 1303 + 1853.
The square root of 3275 is 57.227...., and 57 = 22 + 22 + 72.
32752 = 10725625, 12 + 02 + 72 + 22 + 52 + 62 + 22 + 52 = 122.
Page of Squares : First Upload June 11, 2007 ; Last Revised August 10, 2008by Yoshio Mimura, Kobe, Japan
3276
The integral triangle of sides 6643, 15361, 21900 has square area 32762.
Komachi equation: 32762 = 92 * 82 * 72 * 62 + 52 * 42 * 32 * 212.
Page of Squares : First Upload June 11, 2007 ; Last Revised October 11, 2011by Yoshio Mimura, Kobe, Japan
3277
32772 = 95 + 145 + 155 + 175 + 245.
Page of Squares : First Upload August 10, 2008 ; Last Revised August 10, 2008by Yoshio Mimura, Kobe, Japan
3278
32782 = 10745284, a zigzag square.
Page of Squares : First Upload June 11, 2007 ; Last Revised June 11, 2007by Yoshio Mimura, Kobe, Japan
3280
32802 = (22 + 4)(182 + 4)(642 + 4).
Page of Squares : First Upload December 21, 2013 ; Last Revised December 21, 2013by Yoshio Mimura, Kobe, Japan
3284
(32842 + 8) = (12 + 8)(32 + 8)(42 + 8)(52 + 8)(92 + 8).
Page of Squares : First Upload June 11, 2007 ; Last Revised June 11, 2007by Yoshio Mimura, Kobe, Japan
3286
32863 = 35481557656, and 32 + 52 + 42 + 82 + 12 + 552 + 72 + 62 + 52 + 62 = 3286.
32865 = 383122621331726176, and 32 + 82 + 32 + 122 + 262 + 22 + 12 + 332 + 172 + 262 + 172 + 62 = 3286.
Page of Squares : First Upload December 1, 2008 ; Last Revised December 8, 2008by Yoshio Mimura, Kobe, Japan
3287
32872 = 144 + 184 + 184 + 574.
Page of Squares : First Upload August 10, 2008 ; Last Revised August 10, 2008by Yoshio Mimura, Kobe, Japan
3289
32892 = S2(246) + S2(259), where S2(n) = 12 + 22 + 32 + 42 + ... + n2.
Page of Squares : First Upload June 11, 2007 ; Last Revised June 11, 2007by Yoshio Mimura, Kobe, Japan
3290
32902 = 10824100, 10 + 82 * 4 * 10 + 0 = 10 * 82 * 4 + 10 + 0 = 3290.
Page of Squares : First Upload June 11, 2007 ; Last Revised June 11, 2007by Yoshio Mimura, Kobe, Japan
3292
32922 = 10837264, a zigzag square with different digits.
Komachi equations:
32922 = 98762 * 52 * 42 / 32 / 22 / 102 = 98762 / 52 / 42 / 32 * 22 * 102.
by Yoshio Mimura, Kobe, Japan
3293
32932 = 10843849, 1084 * 3 + 8 * 4 + 9 = 1084 * 3 - 8 + 49 = 3293.
Page of Squares : First Upload June 11, 2007 ; Last Revised June 11, 2007by Yoshio Mimura, Kobe, Japan
3294
32942 = 953 + 1483 + 1893.
Page of Squares : First Upload August 10, 2008 ; Last Revised August 10, 2008by Yoshio Mimura, Kobe, Japan