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6200 - 6299

6200

62002 = 473 + 1453 + 3283 = 2203 + 2303 + 2503.

Page of Squares : First Upload September 26, 2008 ; Last Revised September 26, 2008
by Yoshio Mimura, Kobe, Japan

6201

62012 = 1433 + 2253 + 2893.

62012 = 38452401, a zigzag square.

Page of Squares : First Upload February 4, 2008 ; Last Revised September 26, 2008
by Yoshio Mimura, Kobe, Japan

6202

62022 = 93 + 1473 + 3283.

62022 = 38464804, a zigzag square.

The square root of 6202 is 78.752..., and 78 = 72 + 52 + 22.

Page of Squares : First Upload February 4, 2008 ; Last Revised September 26, 2008
by Yoshio Mimura, Kobe, Japan

6203

1 / 6203 = 0.0001612123166209, 162 + 12 + 22 + 122 + 312 + 662 + 202 + 92 = 6203,
1 / 6203 = 0.0001612123166209, 162 + 122 + 12 + 22 + 312 + 662 + 202 + 92 = 6203.

Page of Squares : First Upload February 4, 2008 ; Last Revised February 4, 2008
by Yoshio Mimura, Kobe, Japan

6204

62042 = 1643 + 1993 + 2973.

6204k + 7050k + 52593k + 113082k are squares for k = 1,2,3 (4232, 1250672, 399011672).

Page of Squares : First Upload September 26, 2008 ; Last Revised June 28, 2011
by Yoshio Mimura, Kobe, Japan

6205

6205 = 382 + 692 and 3869 = 622 + 052.

Page of Squares : First Upload October 9, 2008 ; Last Revised October 9, 2008
by Yoshio Mimura, Kobe, Japan

6208

62082 = 324 + 484 + 484 + 724.

Page of Squares : First Upload September 26, 2008 ; Last Revised September 26, 2008
by Yoshio Mimura, Kobe, Japan

6209

62092 = 38551681, and 32 + 82 + 52 + 52 + 12 + 62 + 82 + 12 = 152.

Page of Squares : First Upload February 4, 2008 ; Last Revised February 4, 2008
by Yoshio Mimura, Kobe, Japan

6210

62102 = (12 + 5)(82 + 5)(152 + 5)(202 + 5).

62102 = 993 + 1533 + 3243.

The integral triangle of sides 6058, 13625, 16767 (or 6458, 14283, 18625) has square area 62102.

Page of Squares : First Upload September 26, 2008 ; Last Revised January 4, 2014
by Yoshio Mimura, Kobe, Japan

6211

62113 = 239598771931, and 22 + 392 + 592 + 82 + 72 + 72 + 12 + 92 + 312 = 6211.

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

6213

62132 = 163 + 1443 + 3293 = 813 + 2663 + 2683.

Page of Squares : First Upload September 26, 2008 ; Last Revised September 26, 2008
by Yoshio Mimura, Kobe, Japan

6214

62142 = (12 + 22 + 32 + ... + 285602)/(12 + 22 + 32 + ... + 842).

Page of Squares : First Upload September 1, 2011 ; Last Revised September 1, 2011
by Yoshio Mimura, Kobe, Japan

6215

62152 = 333 + 1583 + 3263 = 1373 + 2303 + 2883.

Page of Squares : First Upload September 26, 2008 ; Last Revised September 26, 2008
by Yoshio Mimura, Kobe, Japan

6216

62162 = (12 + 3)(22 + 3)(32 + 3)(162 + 3)(212 + 3) = (12 + 3)(92 + 3)(162 + 3)(212 + 3)
= (32 + 3)(52 + 3)(162 + 3)(212 + 3).

62162 = 38638656, 3 * 86 * 3 * 8 + 6 * 5 - 6 = 3 * 86 * 3 * 8 - 6 + 5 * 6 = 6216.

6216k + 18426k + 34521k + 51726k are squares for k = 1,2,3 (3332, 651572, 136393472).

Page of Squares : First Upload February 4, 2008 ; Last Revised January 4, 2014
by Yoshio Mimura, Kobe, Japan

6221

62215 = 9317534440441395101 :
92 + 32 + 172 + 52 + 342 + 42 + 42 + 02 + 442 + 12 + 32 + 92 + 512 + 02 + 12
= 92 + 32 + 172 + 52 + 342 + 442 + 02 + 42 + 42 + 12 + 32 + 92 + 512 + 02 + 12 = 6221.

Page of Squares : First Upload December 8, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

6222

62222 = 1013 + 1833 + 3163 = 274 + 474 + 534 + 714.

Page of Squares : First Upload September 26, 2008 ; Last Revised September 26, 2008
by Yoshio Mimura, Kobe, Japan

6224

62242 = 363 + 1283 + 3323.

62242 = 38738176, 3 - 8 + 73 + 81 * 76 = 3 + 8 * 775 - 5 + 29 = 6227.

Page of Squares : First Upload February 4, 2008 ; Last Revised September 26, 2008
by Yoshio Mimura, Kobe, Japan

6228

62282± 5 are primes.

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

6229

62292 = 973 + 1483 + 3263.

Page of Squares : First Upload September 26, 2008 ; Last Revised September 26, 2008
by Yoshio Mimura, Kobe, Japan

6231

62312 = 35 + 95 + 135 + 255 + 315.

Page of Squares : First Upload September 26, 2008 ; Last Revised September 26, 2008
by Yoshio Mimura, Kobe, Japan

6232

62322 = 683 + 2643 + 2723.

266k + 6232k + 10070k + 12673k are squares for k = 1,2,3 (1712, 173472, 18161912).

Page of Squares : First Upload September 26, 2008 ; Last Revised June 28, 2011
by Yoshio Mimura, Kobe, Japan

6237

62372 = 643 + 893 + 3363.

62372 = S2(50) + S2(488), where S2(n) = 12 + 22 + 32 + 42 + ... + n2.

62372 = (158 + 159 + 160 + 161 + 162 + 163 + 164 + 165 + 166)2 + (167 + 168 + 169 + 170 + 171 + 172 + 173 + 174 + 175)2 + (176 + 177 + 178 + 179 + 180 + 181 + 182 + 183 + 184)2 + ... + (248 + 249 + 250 + 251 + 252 + 253 + 254 + 255 + 256)2.

The sum of the squares of divisors of 6237 is a square, 67102.

Page of Squares : First Upload February 4, 2008 ; Last Revised November 1, 2011
by Yoshio Mimura, Kobe, Japan

6238

62382 = 713 + 1093 + 3343.

Page of Squares : First Upload September 26, 2008 ; Last Revised September 26, 2008
by Yoshio Mimura, Kobe, Japan

6239

The longest chain of length 111 for abcd -- pqrs, whrer abcd2=xypqrsuv :
6239 -- 9251 -- 5810 -- 7561 -- 1687 -- 8459 -- 5546 -- 7581 -- 4715 -- 2312 -- 3453 -- 9232 -- 2298 -- 2808 -- -- 8848 -- 2871 -- 2426 -- 8854 -- 3933 -- 4684 -- 9398 -- 3224 -- 3941 -- 5314 -- 2385 -- 6882 -- 3619 -- 0971 -- 9428 -- 8871 -- 6946 -- -- 2469 -- 0959 -- 9196 -- 5664 -- 0808 -- 6528 -- 6147 -- 7856 -- 7167 -- 3658 -- 3809 -- 5084 -- 8470 -- 7409 -- 8932 -- 7806 -- 9336 -- -- 1608 -- 5856 -- 2927 -- 5673 -- 1829 -- 3452 -- 9163 -- 9605 -- 2560 -- 5536 -- 6472 -- 8867 -- 6236 -- 8876 -- 7833 -- 3558 -- 6593 -- -- 4676 -- 8649 -- 8052 -- 8347 -- 6724 -- 2121 -- 4986 -- 8601 -- 9772 -- 4919 -- 1965 -- 8612 -- 1665 -- 7722 -- 6292 -- 5892 -- 7156 -- -- 2083 -- 3388 -- 4785 -- 8962 -- 3174 -- 0742 -- 5505 -- 3050 -- 3025 -- 1506 -- 2680 -- 1824 -- 3269 -- 6863 -- 1007 -- 0140 -- 0196 -- -- 0384 -- 1474 -- 1726 -- 9790 -- 8441 -- 2504 -- 2700 -- 2900 -- 4100 -- 8100 -- 6100 -- 2100 -- 4100 -- ... (Loop).

Page of Squares : First Upload February 4, 2008 ; Last Revised February 4, 2008
by Yoshio Mimura, Kobe, Japan

6240

62402 = (22 - 1)(32 - 1)(252 - 1)(512 - 1) = (52 - 1)(252 - 1)(512 - 1).

892 + 6240 = 1192, 892 - 6240 = 412.

Komachi equation: 62402 = 12 * 22 * 32 * 42 * 52 * 62 * 782 / 92.

Page of Squares : First Upload October 29, 2010 ; Last Revised January 4, 2014
by Yoshio Mimura, Kobe, Japan

6241

The square of 79.

Page of Squares : First Upload February 4, 2008 ; Last Revised February 4, 2008
by Yoshio Mimura, Kobe, Japan

6243

62432 = 1533 + 2323 + 2843.

Page of Squares : First Upload September 26, 2008 ; Last Revised September 26, 2008
by Yoshio Mimura, Kobe, Japan

6244

62442 = 38987536, 3 + 8 * 9 * 87 - 5 - 3 * 6 = 6244.

62442 = (12 + 3)(52 + 3)(5902 + 3).

Page of Squares : First Upload February 4, 2008 ; Last Revised January 4, 2014
by Yoshio Mimura, Kobe, Japan

6245

A cubic polynomoal :
(X + 14402)(X + 16122)(X + 58592) = X3 + 62452X2 + 128752922X + 136003795202.

Page of Squares : First Upload February 4, 2008 ; Last Revised February 4, 2008
by Yoshio Mimura, Kobe, Japan

6247

62472 = 174 + 464 + 464 + 744.

Page of Squares : First Upload September 26, 2008 ; Last Revised September 26, 2008
by Yoshio Mimura, Kobe, Japan

6248

62482 = (12 + 7)(22 + 7)(82 + 7)(792 + 7) = (12 + 7)(22092 + 7) = (82 + 7)(92 + 7)(792 + 7)
= (14 + 7)(474 + 7).

Page of Squares : First Upload January 4, 2014 ; Last Revised January 4, 2014
by Yoshio Mimura, Kobe, Japan

6250

62502 = 1023 + 2513 + 2813 = 255 + 255 + 255 + 255.

62502 = 39062500, 3 * 9 * 0 + 6250 + 0 = 3 / 9 * 0 + 6250 + 0 = 39 * 0 + 6250 + 0 = 6250.

Page of Squares : First Upload February 4, 2008 ; Last Revised September 26, 2008
by Yoshio Mimura, Kobe, Japan

6251

62515 = 9544375000390656251 :
and 92 + 52 + 42 + 42 + 372 + 502 + 02 + 02 + 392 + 02 + 62 + 52 + 62 + 252 + 12 = 6251.

Page of Squares : First Upload December 8, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

6252

62522 = 39087504, 3 * 908 + 7 * 504 = 6252.

Page of Squares : First Upload February 4, 2008 ; Last Revised February 4, 2008
by Yoshio Mimura, Kobe, Japan

6253

62532 = 3032 + 3052 + 3072 + 3092 + 3112 + 3132 + ... + 6392.

260k + 286k + 1742k + 5993k are squares for k = 1,2,3 (912, 62532, 4696512).

Page of Squares : First Upload February 4, 2008 ; Last Revised June 28, 2011
by Yoshio Mimura, Kobe, Japan

6254

62542 = 1123 + 1133 + 3313.

Page of Squares : First Upload September 26, 2008 ; Last Revised September 26, 2008
by Yoshio Mimura, Kobe, Japan

6256

62562 = 39137536, a square with odd digits except the last digit 6.

Page of Squares : First Upload August 24, 2013 ; Last Revised August 24, 2013
by Yoshio Mimura, Kobe, Japan

6258

62582± 5 are primes.

62582 = (32 + 5)(122 + 5)(1372 + 5).

62582 = 823 + 1193 + 3333.

The square root of 6258 is 79.10752...., and 79 = 12 + 02 + 72 + 52 + 22.

62582 = 39162564, 39 * 162 - 56 - 4 = 6258.

Page of Squares : First Upload February 4, 2008 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

6260

Loop of length 56 by the function f(N) = ... + c2 + b2 + a2 where N = ... + 1002c + 100b + a:
6260 - 7444 - 7412 - 5620 - ... - 9738 - 10853 - 2874 - 6260
(Note f(6260) = 622 + 602 = 7444,   f(7444) = 742 + 442 = 7412, etc. See 41)

Page of Squares : First Upload October 9, 2008 ; Last Revised October 9, 2008
by Yoshio Mimura, Kobe, Japan

6261

62612 = 563 + 2463 + 2893.

62612 = 39200121, 32 + 92 + 22 + 02 + 02 + 12 + 22 + 12 = 102.

Page of Squares : First Upload February 4, 2008 ; Last Revised September 26, 2008
by Yoshio Mimura, Kobe, Japan

6263

1 / 6263 = 0.0001596678, 12 + 52 + 92 + 62 + 62 + 782 = 6263.

Page of Squares : First Upload February 4, 2008 ; Last Revised February 4, 2008
by Yoshio Mimura, Kobe, Japan

6264

62642 = 183 + 1583 + 3283.

Komachi equations:
62642 = 92 * 872 * 62 * 52 * 42 / 32 * 22 / 102 = 92 * 872 * 62 / 52 * 42 / 32 / 22 * 102
 = 92 * 872 / 62 / 52 * 42 * 32 * 22 * 102.

Page of Squares : First Upload September 26, 2008 ; Last Revised October 29, 2010
by Yoshio Mimura, Kobe, Japan

6266

62662 = 39262756, a zigzag square.

62662 = 39262756, and 3 - 9 * 2 + 6275 + 6 = 6266.

Page of Squares : First Upload February 4, 2008 ; Last Revised February 4, 2008
by Yoshio Mimura, Kobe, Japan

6267

62672 = 39275289, 39 - 2 + 7 * 5 * 2 * 89 = 6267.

Page of Squares : First Upload February 4, 2008 ; Last Revised February 4, 2008
by Yoshio Mimura, Kobe, Japan

6268

62682 = 353 + 1493 + 3303.

62682 = 39287824, a zigzag square.

Page of Squares : First Upload February 4, 2008 ; Last Revised September 26, 2008
by Yoshio Mimura, Kobe, Japan

6269

Loop of length 5 :   6269 --- 622 + 692 = 8605 --- 862 + 052 = 7421 --- 722 + 412 = 5917 --- 592 + 172 = 3770 -- 372 + 702 = 6269

Page of Squares : First Upload October 9, 2008 ; Last Revised October 9, 2008
by Yoshio Mimura, Kobe, Japan

6270

1330k + 3610k + 5690k + 6270k are squares for k = 1,2,3 (1302, 93002, 6929002).

Page of Squares : First Upload June 28, 2011 ; Last Revised June 28, 2011
by Yoshio Mimura, Kobe, Japan

6272

62722 = 1123 + 3363 = 163 + 2243 + 3043 = 564 + 564 + 564 + 564.

Page of Squares : First Upload September 26, 2008 ; Last Revised September 26, 2008
by Yoshio Mimura, Kobe, Japan

6273

62732 = 64 + 124 + 394 + 784.

62732 = 39350529, a zigzag square.

Page of Squares : First Upload February 4, 2008 ; Last Revised September 26, 2008
by Yoshio Mimura, Kobe, Japan

6274

62744 = 1549451752181776,
and 12 + 52 + 42 + 92 + 42 + 52 + 12 + 72 + 52 + 22 + 12 + 82 + 12 + 772 + 62 = 6274.

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

6275

62752 = 39375625, a zigzag square.

62752 = S2(305) + S2(447), where S2(n) = 12 + 22 + 32 + 42 + ... + n2.

Page of Squares : First Upload February 4, 2008 ; Last Revised February 4, 2008
by Yoshio Mimura, Kobe, Japan

6278

62782± 3 are primes.

62782 = 1133 + 2583 + 2753.

62784 = 1553406955664656,
and 12 + 52 + 532 + 42 + 02 + 62 + 92 + 52 + 52 + 62 + 62 + 42 + 62 + 562 = 6278,
and 12 + 52 + 532 + 42 + 02 + 62 + 92 + 52 + 562 + 62 + 42 + 62 + 52 + 62 = 6278.

Page of Squares : First Upload September 26, 2008 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

6279

6279 = (12 + 22 + 32 + ... + 452) / (12 + 22).

Page of Squares : First Upload November 25, 2008 ; Last Revised November 25, 2008
by Yoshio Mimura, Kobe, Japan

6280

62802± 3 are primes.

62802 = 2804 x 2805 + 2806 x 2807 + 2808 x 2809 + 2810 x 2811 + ... + 2812 x 2813.

62803 = 247673152000, and 22 + 42 + 762 + 72 + 32 + 12 + 52 + 202 + 02 + 02 = 6280.

Page of Squares : First Upload February 4, 2008 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

6282

62822 = 39463524, a zigzag square.

62822 = 39463524, and 32 + 92 + 42 + 62 + 32 + 52 + 22 + 42 = 142.

Page of Squares : First Upload February 4, 2008 ; Last Revised February 4, 2008
by Yoshio Mimura, Kobe, Japan

6283

62832 = 643 + 983 + 3373.

Page of Squares : First Upload September 26, 2008 ; Last Revised September 26, 2008
by Yoshio Mimura, Kobe, Japan

6286

62862 = 39513796, a square with odd digits except the last digit 6.

Page of Squares : First Upload August 24, 2013 ; Last Revised August 24, 2013
by Yoshio Mimura, Kobe, Japan

6288

62882 = 623 + 2203 + 3063 = 244 + 324 + 644 + 684.

Page of Squares : First Upload September 26, 2008 ; Last Revised September 26, 2008
by Yoshio Mimura, Kobe, Japan

6289

152k + 209k + 3344k + 5320k are squares for k = 1,2,3 (952, 62892, 4335612).

Page of Squares : First Upload June 28, 2011 ; Last Revised June 28, 2011
by Yoshio Mimura, Kobe, Japan

6290

6290 = (12 + 22 + 32 + ... + 41992) / (12 + 22 + 32 + ... + 2272).

62902 = (12 + 1)(22 + 1)(62 + 1)(3272 + 1) = (12 + 1)(382 + 1)(1172 + 1)
= (32 + 1)(62 + 1)(3272 + 1) = (42 + 1)(132 + 1)(1172 + 1) = (52 + 9)(192 + 9)(562 + 9).

62902 = 1633 + 2463 + 2733.

3441k + 6290k + 10138k + 14356k are squares for k = 1,2,3 (1852, 189812, 20712972).

Page of Squares : First Upload September 26, 2008 ; Last Revised January 4, 2014
by Yoshio Mimura, Kobe, Japan

6291

62912 = 39576681, 3 * 9 * 5 * 7 + 66 * 81 = 6291.

Page of Squares : First Upload February 4, 2008 ; Last Revised February 4, 2008
by Yoshio Mimura, Kobe, Japan

6292

62922 = 1543 + 3303 = 113 + 2533 + 2863.

Page of Squares : First Upload September 26, 2008 ; Last Revised September 26, 2008
by Yoshio Mimura, Kobe, Japan

6294

62942 = 673 + 2223 + 3053.

Page of Squares : First Upload September 26, 2008 ; Last Revised September 26, 2008
by Yoshio Mimura, Kobe, Japan

6296

62962 = 563 + 1763 + 3243.

62962 = 39639616, and 32 + 92 + 62 + 32 + 92 + 62 + 12 + 62 = 172.

62962 = 39639616, and 3 * 9 * 6 * 39 - 6 - 16 = 6296 = 39 * 6 * 3 * 9 - 6 - 16 = 6296.

Page of Squares : First Upload February 4, 2008 ; Last Revised September 26, 2008
by Yoshio Mimura, Kobe, Japan

6297

1 / 6297 = 0.00015880578053, 12 + 52 + 82 + 82 + 052 + 782 + 052 + 32 = 6297.

The square root of 6297 is 79.3536...., and 79 = 32 + 52 + 32 + 62.

Page of Squares : First Upload February 4, 2008 ; Last Revised February 4, 2008
by Yoshio Mimura, Kobe, Japan