5200
52002 = (12 + 4)(102 + 4)(142 + 4)(162 + 4) = (12 + 4)(22 + 4)(32 + 4)(142 + 4)(162 + 4)
= (12 + 4)(22 + 4)(32 + 4)(62 + 4)(362 + 4) = (12 + 4)(22 + 4)(42 + 4)(62 + 4)(292 + 4)
= (12 + 4)(32 + 4)(42 + 4)(102 + 4)(142 + 4) = (12 + 4)(62 + 4)(102 + 4)(362 + 4)
= (102 + 4)(142 + 4)(362 + 4) = (22 + 4)(102 + 4)(112 + 4)(162 + 4) = (22 + 4)(162 + 4)(1142 + 4)
= (22 + 4)(32 + 4)(142 + 4)(362 + 4) = (22 + 4)(32 + 4)(42 + 4)(102 + 4)(112 + 4)
= (22 + 4)(32 + 4)(42 + 4)(1142 + 4) = (22 + 4)(42 + 4)(142 + 4)(292 + 4)
= (32 + 4)(62 + 4)(142 + 4)(162 + 4) = (42 + 4)(102 + 4)(1142 + 4).
by Yoshio Mimura, Kobe, Japan
5201
52012 = 383 + 2173 + 2563.
52012 = 27050401, a zigzag square.
Page of Squares : First Upload November 5, 2007 ; Last Revised September 16, 2008by Yoshio Mimura, Kobe, Japan
5202
52022 = 514 + 514 + 514 + 514.
52022 = 27060804, a zigzag square.
52022 = 27060804, 22 + 72 + 02 + 62 + 02 + 82 + 02 + 42 = 132.
Page of Squares : First Upload November 5, 2007 ; Last Revised September 16, 2008by Yoshio Mimura, Kobe, Japan
5203
52032 = 27071209, a zigzag square.
Page of Squares : First Upload November 5, 2007 ; Last Revised November 5, 2007by Yoshio Mimura, Kobe, Japan
5204
52042 = 27081616, a zigzag square.
Page of Squares : First Upload November 5, 2007 ; Last Revised November 5, 2007by Yoshio Mimura, Kobe, Japan
5205
52052 = 43 + 1053 + 2963.
Page of Squares : First Upload September 16, 2008 ; Last Revised September 16, 2008by Yoshio Mimura, Kobe, Japan
5207
5207 = (12 + 22 + 32 + ... + 110492) / (12 + 22 + 32 + ... + 6372).
52072 = 533 + 2373 + 2393 = 74 + 464 + 584 + 584.
Page of Squares : First Upload September 16, 2008 ; Last Revised November 25, 2008by Yoshio Mimura, Kobe, Japan
5208
52082 = (12 + 3)(32 + 3)(92 + 3)(822 + 3) = (22 + 3)(32 + 3)(112 + 3)(512 + 3)
= (32 + 3)(112 + 3)(1352 + 3) = (92 + 3)(112 + 3)(512 + 3).
by Yoshio Mimura, Kobe, Japan
5209
A cubic polynomial :
(X + 10442)(X + 26392)(X + 43682) = X3 + 52092X2 + 126988682X + 120343466882.
by Yoshio Mimura, Kobe, Japan
5211
52112 = 723 + 1863 + 2733.
Page of Squares : First Upload September 16, 2008 ; Last Revised September 16, 2008by Yoshio Mimura, Kobe, Japan
5216
52162 = 1443 + 1883 + 2603.
Page of Squares : First Upload September 16, 2008 ; Last Revised September 16, 2008by Yoshio Mimura, Kobe, Japan
5217
52172 = 244 + 384 + 434 + 684.
The square root of 5217 is 72.228..., and 72 = 22 + 22 + 82.
Page of Squares : First Upload November 5, 2007 ; Last Revised September 16, 2008by Yoshio Mimura, Kobe, Japan
5220
52202 = (12 + 9)(32 + 9)(72 + 9)(512 + 9).
Komachi equations:
52202 = 92 * 872 / 62 * 52 / 42 * 322 */ 12 = 92 * 872 * 62 / 542 * 32 * 22 * 102.
by Yoshio Mimura, Kobe, Japan
5221
52212 = 27258841 appears in the decimal expressions of π:
π = 3.14159•••27258841••• (from the 32175th digit)
(27258841 is the sixth 8-digit square in the expression of π.)
by Yoshio Mimura, Kobe, Japan
5223
52232 = 27279729, a zigzag square.
Page of Squares : First Upload November 5, 2007 ; Last Revised November 5, 2007by Yoshio Mimura, Kobe, Japan
5225
52255 = 3894318555166015625 : 32 + 82 + 92 + 42 + 32 + 182 + 52 + 52 + 52 + 12 + 662 + 02 + 152 + 62 + 22 + 52 = 5225.
Page of Squares : First Upload December 8, 2008 ; Last Revised December 8, 2008by Yoshio Mimura, Kobe, Japan
5226
1326k + 2730k + 5226k + 7618k are squares for k = 1,2,3 (1302, 97242, 7794282).
Page of Squares : First Upload June 17, 2011 ; Last Revised June 17, 2011by Yoshio Mimura, Kobe, Japan
5229
52292 = 1203 + 1743 + 2733.
52292 = 27342441, 2 * 7 * 342 + 441 = 5229.
Page of Squares : First Upload November 5, 2007 ; Last Revised September 16, 2008by Yoshio Mimura, Kobe, Japan
5232
52322 = 35 + 95 + 205 + 255 + 275.
52322 = 27373824, a zigzag square.
Komachi equation: 52322 = 92 * 82 * 72 * 6542 / 32 / 212.
52322 = 27373824, 2 * 7 * 373 + 8 - 2 + 4 = 27 / 3 * 73 * 8 - 24 = 5232.
Page of Squares : First Upload November 5, 2007 ; Last Revised October 19, 2010by Yoshio Mimura, Kobe, Japan
5234
52342 = 27394756, a zigzag square.
Page of Squares : First Upload November 5, 2007 ; Last Revised November 5, 2007by Yoshio Mimura, Kobe, Japan
5235
52352 = 13 + 743 + 3003.
52352 = 27405225, 2 * 7 - 4 + 0 + 5225 = 5235.
Page of Squares : First Upload November 5, 2007 ; Last Revised September 16, 2008by Yoshio Mimura, Kobe, Japan
5237
52372 = 1983 + 2013 + 2263.
Page of Squares : First Upload September 16, 2008 ; Last Revised September 16, 2008by Yoshio Mimura, Kobe, Japan
5238
52382 = 1293 + 2223 + 2433.
Komachi equations: 52382 = 92 / 82 / 72 * 62 * 54322 */ 12.
Page of Squares : First Upload September 16, 2008 ; Last Revised October 19, 2010by Yoshio Mimura, Kobe, Japan
5240
52402 = 27457600, 2 * 74 * 5 * 7 + 60 + 0 = 5240.
Page of Squares : First Upload November 5, 2007 ; Last Revised November 5, 2007by Yoshio Mimura, Kobe, Japan
5242
52422 = 83 + 2193 + 2573.
Page of Squares : First Upload September 16, 2008 ; Last Revised September 16, 2008by Yoshio Mimura, Kobe, Japan
5243
52432 = 773 + 2313 + 2453.
Page of Squares : First Upload September 16, 2008 ; Last Revised September 16, 2008by Yoshio Mimura, Kobe, Japan
5244
52442 = 1223 + 1863 + 2683.
52442 = 27499536, 2 - 7 - 4 + 99 * 53 + 6 = 5244.
Page of Squares : First Upload November 5, 2007 ; Last Revised September 16, 2008by Yoshio Mimura, Kobe, Japan
5246
52462 = 27520516, 22 + 72 + 52 + 22 + 02 + 52 + 12 + 62 = 122.
52462 = (132 + 3)(4002 + 3).
Page of Squares : First Upload November 5, 2007 ; Last Revised December 28, 2013by Yoshio Mimura, Kobe, Japan
5247
52472 = 124 + 184 + 274 + 724.
52472 = 27531009, 22 + 72 + 52 + 32 + 12 + 02 + 02 + 92 = 132.
Page of Squares : First Upload November 5, 2007 ; Last Revised September 16, 2008by Yoshio Mimura, Kobe, Japan
5248
52482 = 84 + 244 + 244 + 724.
Page of Squares : First Upload September 16, 2008 ; Last Revised September 16, 2008by Yoshio Mimura, Kobe, Japan
5250
52502 = (12 + 6)(122 + 6)(1622 + 6) = (12 + 6)(22 + 6)(32 + 6)(122 + 6)(132 + 6)
= (12 + 6)(22 + 6)(32 + 6)(1622 + 6) = (32 + 6)(82 + 6)(122 + 6)(132 + 6)
= (32 + 6)(82 + 6)(1622 + 6).
by Yoshio Mimura, Kobe, Japan
5251
5251k + 7257k + 15635k + 27553k are squares for k = 1,2,3 (2362, 329222, 50265642).
Page of Squares : First Upload June 17, 2011 ; Last Revised June 17, 2011by Yoshio Mimura, Kobe, Japan
5252
52522 = 27583504, a zigzag square.
Page of Squares : First Upload November 5, 2007 ; Last Revised November 5, 2007by Yoshio Mimura, Kobe, Japan
5253
52532 = 27594009, 22 + 72 + 52 + 92 + 42 + 02 + 02 + 92 = 162.
52532 + 52542 + 52552 + ... + 53042 = 53052 + 53062 + 53072 + ... + 53552.
Page of Squares : First Upload November 5, 2007 ; Last Revised September 16, 2011by Yoshio Mimura, Kobe, Japan
5255
52552 = 27615025, 22 + 72 + 62 + 12 + 52 + 02 + 22 + 52 = 122.
Page of Squares : First Upload November 5, 2007 ; Last Revised November 5, 2007by Yoshio Mimura, Kobe, Japan
5256
52562± 5 are primes.
52562 = 723 + 1423 + 2903.
52562 = 27625536, 2 * 7 * 625 / 5 * 3 + 6 = 5256.
Page of Squares : First Upload November 5, 2007 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
5257
52572 = 1933 + 2013 + 2313.
Page of Squares : First Upload September 16, 2008 ; Last Revised September 16, 2008by Yoshio Mimura, Kobe, Japan
5258
1276k + 1529k + 1738k + 5258k are squares for k = 1,2,3 (992, 58852, 3953072).
Page of Squares : First Upload June 17, 2011 ; Last Revised June 17, 2011by Yoshio Mimura, Kobe, Japan
5259
Komachi equation: 52592 = 92 * 87652 * 42 / 32 / 22 / 102.
Page of Squares : First Upload October 19, 2010 ; Last Revised October 19, 2010by Yoshio Mimura, Kobe, Japan
5265
52652 = 333 + 1563 + 2883.
Komachi equation: 52652 = 122 * 32 / 42 * 52 / 62 * 782 * 92.
Page of Squares : First Upload September 16, 2008 ; Last Revised October 19, 2010by Yoshio Mimura, Kobe, Japan
5270
1666k + 2210k + 5270k + 9350k are squares for k = 1,2,3 (1362, 110842, 9895362).
496k + 5270k + 7161k + 11098k are squares for k = 1,2,3 (1552, 142292, 13713472).
by Yoshio Mimura, Kobe, Japan
5273
1 / 5273 = 0.0001896453631, 12 + 82 + 92 + 642 + 52 + 32 + 62 + 312 = 5273.
Page of Squares : First Upload November 5, 2007 ; Last Revised November 5, 2007by Yoshio Mimura, Kobe, Japan
5277
52772 = 253 + 663 + 3023.
Page of Squares : First Upload September 16, 2008 ; Last Revised September 16, 2008by Yoshio Mimura, Kobe, Japan
5278
52782 = 573 + 983 + 2993.
Page of Squares : First Upload September 16, 2008 ; Last Revised September 16, 2008by Yoshio Mimura, Kobe, Japan
5280
52802 = (112 - 1)(212 - 1)(232 - 1) = (32 - 1)(212 - 1)(892 - 1) = (32 - 1)(42 - 1)(212 - 1)(232 - 1)
= (32 - 1)(92 - 1)(102 - 1)(212 - 1) = (42 - 1)(212 - 1)(652 - 1).
52802 = 1453 + 1463 + 2793.
The integral triangle of sides 697, 131144, 131697 has square area 52802.
1222 + 5280 = 1422, 1222 - 5280 = 982,
732 + 5280 = 1032, 732 - 5280 = 72.
The square root of 5280 is 72.66..., 72 = 62 + 62.
Page of Squares : First Upload November 5, 2007 ; Last Revised December 28, 2013by Yoshio Mimura, Kobe, Japan
5281
52812 = 27888961, 2 - 7 * 8 + 889 * 6 + 1 = 5281.
Page of Squares : First Upload November 5, 2007 ; Last Revised November 5, 2007by Yoshio Mimura, Kobe, Japan
5282
52822 = 27899524, 22 + 72 + 82 + 92 + 92 + 52 + 22 + 42 = 182.
Page of Squares : First Upload November 5, 2007 ; Last Revised November 5, 2007by Yoshio Mimura, Kobe, Japan
5283
52832 = 663 + 2203 + 2573 = 1293 + 1783 + 2723.
Page of Squares : First Upload September 16, 2008 ; Last Revised September 16, 2008by Yoshio Mimura, Kobe, Japan
5286
52862± 5 are primes.
52862 = (22 + 2)(21582 + 2).
Page of Squares : First Upload December 28, 2013 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
5287
52872 = 27952369, 22 + 72 + 92 + 52 + 22 + 32 + 62 + 92 = 172.
Page of Squares : First Upload November 5, 2007 ; Last Revised November 5, 2007by Yoshio Mimura, Kobe, Japan
5288
52882 = 27962944, 27 / 9 * 6 * 294 - 4 = 5288.
Page of Squares : First Upload November 5, 2007 ; Last Revised November 5, 2007by Yoshio Mimura, Kobe, Japan
5289
52892 = (62 + 5)(8262 + 5).
5289k + 9202k + 12986k + 18748k are squares for k = 1,2,3 (2152, 251552, 31155652).
Page of Squares : First Upload June 17, 2011 ; Last Revised December 28, 2013by Yoshio Mimura, Kobe, Japan
5292
52922 = (12 + 5)(22 + 5)(32 + 5)(112 + 5)(172 + 5) = (12 + 5)(32 + 5)(42 + 5)(72 + 5)(172 + 5)
= (32 + 5)(72 + 5)(112 + 5)(172 + 5).
52922 = 843 + 1263 + 2943 = 1023 + 2223 + 2523.
52922 = 28005264, 28 + 0 + 0 + 5264 = 28 + 0 * 0 + 5264 = 5292.
Page of Squares : First Upload November 5, 2007 ; Last Revised December 28, 2013by Yoshio Mimura, Kobe, Japan
5294
52942 = 28026436, 22 + 82 + 02 + 22 + 62 + 42 + 32 + 62 = 132.
Page of Squares : First Upload November 5, 2007 ; Last Revised November 5, 2007by Yoshio Mimura, Kobe, Japan
5298
52982 = 28068804, a square with even digits.
Page of Squares : First Upload November 5, 2007 ; Last Revised November 5, 2007by Yoshio Mimura, Kobe, Japan