4500
45002 = 1203 + 2103 + 2103.
Page of Squares : First Upload September 1, 2008 ; Last Revised September 1, 2008by Yoshio Mimura, Kobe, Japan
4501
45012 = 20259001, 2 + 0 - 2 + 5 * 900 + 1 = 2 + 0 * 2 + 5 * 900 - 1 = 2 * 0 + 2 + 5 * 900 - 1
= 2 * 0 * 2 + 5 * 900 + 1 = 20 / 2 * 5 * 90 + 0 + 1 = 20 * 25 * 9 + 0 + 0 + 1
= 20 * 25 * 9 + 0 * 0 + 1 = 4501.
45015 = 1847332473952522501 : 12 + 82 + 42 + 72 + 32 + 32 + 22 + 42 + 72 + 392 + 52 + 22 + 522 + 22 + 52 + 02 + 12 = 12 + 82 + 42 + 72 + 32 + 32 + 22 + 42 + 72 + 392 + 522 + 52 + 22 + 22 + 52 + 02 + 12 = 4501.
Page of Squares : First Upload September 18, 2007 ; Last Revised December 8, 2008by Yoshio Mimura, Kobe, Japan
4502
45022 = 20268004, a square with even digits.
Page of Squares : First Upload September 18, 2007 ; Last Revised September 18, 2007by Yoshio Mimura, Kobe, Japan
4503
45032 = 383 + 1453 + 2583.
Page of Squares : First Upload September 1, 2008 ; Last Revised September 1, 2008by Yoshio Mimura, Kobe, Japan
4504
The square root of 4504 is 67.1118..., and 67 = 12 + 12 + 12 + 82.
Page of Squares : First Upload September 18, 2007 ; Last Revised September 18, 2007by Yoshio Mimura, Kobe, Japan
4507
45075 = 1859678158261539307 : 12 + 82 + 52 + 92 + 62 + 72 + 82 + 152 + 82 + 22 + 612 + 52 + 32 + 92 + 32 + 02 + 72 = 4507.
Page of Squares : First Upload December 8, 2008 ; Last Revised December 8, 2008by Yoshio Mimura, Kobe, Japan
4508
45082 = 633 + 733 + 2703 = 633 + 1773 + 2443 = 144 + 284 + 564 + 564.
45082 = (46 + 47 + 48 + 49 + 50 + 51 + 52)2 + (53 + 54 + 55 + 56 + 57 + 58 + 59)2 + (60 + 61 + 62 + 63 + 64 + 65 + 66)2 + ... + (200 + 201 + 202 + 203 + 204 + 205 + 206)2.
Page of Squares : First Upload September 18, 2007 ; Last Revised September 1, 2008by Yoshio Mimura, Kobe, Japan
4509
45092 = 453 + 1353 + 2613.
Page of Squares : First Upload September 1, 2008 ; Last Revised September 1, 2008by Yoshio Mimura, Kobe, Japan
4511
45112 = 1652 + 1672 + 1692 + 1712 + ... + 5012.
Page of Squares : First Upload September 18, 2007 ; Last Revised September 18, 2007by Yoshio Mimura, Kobe, Japan
4512
45122 = 293 + 1633 + 2523.
The square root of 4512 is 67.1714..., and 67 = 12 + 72 + 12 + 42.
Page of Squares : First Upload September 18, 2007 ; Last Revised September 18, 2007by Yoshio Mimura, Kobe, Japan
4513
45132 = 263 + 1503 + 2573 = 174 + 284 + 564 + 564.
Page of Squares : First Upload September 1, 2008 ; Last Revised September 1, 2008by Yoshio Mimura, Kobe, Japan
4514
45142 = 1373 + 1943 + 2193.
Page of Squares : First Upload September 1, 2008 ; Last Revised September 1, 2008by Yoshio Mimura, Kobe, Japan
4519
45192 = 253 + 393 + 2733.
Page of Squares : First Upload September 1, 2008 ; Last Revised September 1, 2008by Yoshio Mimura, Kobe, Japan
4521
45212 = (52 + 8)(7872 + 8).
Page of Squares : First Upload December 28, 2013 ; Last Revised December 28, 2013by Yoshio Mimura, Kobe, Japan
4522
45222 = 174 + 174 + 194 + 674.
45222 = 20448484, a square with even digits.
45222 = 20448484, 22 + 02 + 42 + 42 + 82 + 42 + 82 + 42 = 142.
Page of Squares : First Upload September 18, 2007 ; Last Revised September 1, 2008by Yoshio Mimura, Kobe, Japan
4523
The square root of 4523 is 67.25325..., and 67 = 22 + 52 + 32 + 22 + 52.
Page of Squares : First Upload September 18, 2007 ; Last Revised September 18, 2007by Yoshio Mimura, Kobe, Japan
4524
609k + 4524k + 6960k + 8932k are squares for k = 1,2,3 (1452, 122092, 10689112).
3190k + 4524k + 13137k + 20358k are squares for k = 1,2,3 (2032, 248532, 32908332).
by Yoshio Mimura, Kobe, Japan
4525
1/4525 = 0.0002209... and 2209 = 472. (the same for 45262).
Page of Squares : First Upload September 18, 2007 ; Last Revised September 18, 2007by Yoshio Mimura, Kobe, Japan
4527
45272 = 64 + 244 + 334 + 664 = 424 + 484 + 484 + 514.
Page of Squares : First Upload September 1, 2008 ; Last Revised September 1, 2008by Yoshio Mimura, Kobe, Japan
4531
A cubic polynomial:
(X + 8282)(X + 26882)(X + 45312) = X3 + 53332X2 + 129369482X + 100844835842.
by Yoshio Mimura, Kobe, Japan
4533
45335 = 1913941217714857893 : 192 + 132 + 92 + 42 + 122 + 12 + 72 + 72 + 142 + 82 + 572 + 82 + 92 + 32 = 4533.
Page of Squares : First Upload December 8, 2008 ; Last Revised December 8, 2008by Yoshio Mimura, Kobe, Japan
4535
45355 = 1918167184754084375 : 12 + 92 + 12 + 82 + 12 + 62 + 72 + 12 + 82 + 472 + 52 + 42 + 02 + 82 + 432 + 72 + 52 = 4535.
Page of Squares : First Upload December 8, 2008 ; Last Revised December 8, 2008by Yoshio Mimura, Kobe, Japan
4536
45362 = 1983 + 2343 = 33 + 1893 + 2403 = 123 + 143 + 2743 = 723 + 2103 + 2223.
Komachi equations:
45362 = 122 * 32 / 42 + 5672 * 82 - 92 = 122 * 32 / 42 * 5672 * 82 / 92
= - 122 * 32 / 42 + 5672 * 82 + 92.
45364 = 423342805487616, and 42 + 22 + 32 + 32 + 422 + 82 + 02 + 52 + 482 + 72 + 62 + 162 = 4536,
45364 = 423342805487616, and 422 + 32 + 32 + 42 + 22 + 82 + 02 + 52 + 482 + 72 + 62 + 162 = 4536.
by Yoshio Mimura, Kobe, Japan
4537
45372 = 283 + 603 + 2733.
45372 = 20584369, a square with different digits.
45374 = 423716247128161, and 422 + 32 + 72 + 12 + 62 + 22 + 472 + 122 + 82 + 162 + 12 = 4537,
45374 = 423716247128161, and 422 + 32 + 72 + 162 + 22 + 472 + 122 + 82 + 12 + 62 + 12 = 4537.
Loop of length 35 by the function f(N) = ... + c2 + b2 + a2 where N = ... + 1002c + 100b + a:
4537 - 3394 - 9925 - 10426 - ... - 5493 - 11565 - 4451 - 4537
(Note f(4537) = 452 + 372 = 3394, f(3394) = 332 + 942 = 9925, etc. See 37)
by Yoshio Mimura, Kobe, Japan
4539
Komachi equation: 45392 = 122 * 342 / 562 * 72 * 892.
Page of Squares : First Upload October 13, 2010 ; Last Revised October 13, 2010by Yoshio Mimura, Kobe, Japan
4542
45422 = 20629764, 2 + 0 + 6 * 2 * 9 * 7 * 6 + 4 = 2 + 0 + 6 + 4 * 7 * 9 * 3 * 6 = 2 + 0 + 6 * 4 * 7 * 9 * 3 + 6 = 4544.
Page of Squares : First Upload September 18, 2007 ; Last Revised September 18, 2007by Yoshio Mimura, Kobe, Japan
4544
45442 = 643 + 643 + 2723 = 963 + 1443 + 2563.
45445 = 1937276514257076224 : 192 + 32 + 72 + 272 + 62 + 512 + 42 + 22 + 52 + 72 + 02 + 72 + 62 + 22 + 242 = 4544.
Page of Squares : First Upload September 1, 2008 ; Last Revised December 8, 2008by Yoshio Mimura, Kobe, Japan
4545
45452 = 483 + 1293 + 2643.
45452 = 20657025, 2 + 0 + 65 * 70 - 2 - 5 = 20 + 65 * 70 - 25 = 4545.
Page of Squares : First Upload September 18, 2007 ; Last Revised September 1, 2008by Yoshio Mimura, Kobe, Japan
4550
45502 = (123 + 124 + 125 + 126 + 127)2 + (128 + 129 + 130 + 131 + 132)2 + (133 + 134 + 135 + 136 + 137)2 + ... + (238 + 239 + 240 + 241 + 242)2.
Page of Squares : First Upload September 18, 2007 ; Last Revised September 18, 2007by Yoshio Mimura, Kobe, Japan
4553
45532 = 1333 + 1493 + 2473.
Page of Squares : First Upload September 1, 2008 ; Last Revised September 1, 2008by Yoshio Mimura, Kobe, Japan
4554
45542 = 20738916, a square with different digits.
3553k + 4554k + 5742k + 6600k are squares for k = 1,2,3 (1432, 104832, 7849272).
667k + 2507k + 2553k + 2737k are squares for k = 1,2,3 (922, 45542, 2306442).
by Yoshio Mimura, Kobe, Japan
4556
45562 = 20757136 appears in the decimal expressions of π:
π = 3.14159•••20757136••• (from the 12943rd digit)
(20757136 is the second 8-digit square in the expression of π.)
by Yoshio Mimura, Kobe, Japan
4558
344k + 1505k + 4558k + 10234k are squares for k = 1,2,3 (1292, 113092, 10816652).
Page of Squares : First Upload June 14, 2011 ; Last Revised June 14, 2011by Yoshio Mimura, Kobe, Japan
4559
45592 = 1523 + 1853 + 2223.
45592 = 20784481, 2 * 0 + 78 + 4481 = 2 + 0 - 84 + 83 * 56 = 4566.
Page of Squares : First Upload September 18, 2007 ; Last Revised September 1, 2008by Yoshio Mimura, Kobe, Japan
4560
Komachi equations: 45602 = 92 * 82 * 762 * 52 / 42 / 32 * 22 */ 12.
Page of Squares : First Upload October 13, 2010 ; Last Revised October 13, 2010by Yoshio Mimura, Kobe, Japan
4562
45622 = 30 + 33 + 34 + 35 + 38 + 39 + 310 + 313 + 314 + 315.
Page of Squares : First Upload August 30, 2011 ; Last Revised August 30, 2011by Yoshio Mimura, Kobe, Japan
4563
45632 = 783 + 2733 = 573 + 1173 + 2673 = 1213 + 1563 + 2483.
Page of Squares : First Upload September 1, 2008 ; Last Revised September 1, 2008by Yoshio Mimura, Kobe, Japan
4568
45682 = 1403 + 1983 + 2183.
45682 = 20866624, a square with even digits.
45682 = 20866624, 22 + 02 + 82 + 62 + 62 + 62 + 22 + 42 = 142.
Page of Squares : First Upload September 18, 2007 ; Last Revised September 1, 2008by Yoshio Mimura, Kobe, Japan
4569
45692 = 20875761, 20 + 8 + 757 * 6 - 1 = 4569.
Page of Squares : First Upload September 18, 2007 ; Last Revised September 18, 2007by Yoshio Mimura, Kobe, Japan
4570
830k + 2010k + 4570k + 4690k are squares for k = 1,2,3 (1102, 69002, 4553002).
Page of Squares : First Upload June 14, 2011 ; Last Revised June 14, 2011by Yoshio Mimura, Kobe, Japan
4572
45722 = 463 + 1343 + 2643 = 723 + 1993 + 2333.
45722 = 20903184, a zigzag square.
Page of Squares : First Upload September 18, 2007 ; Last Revised September 1, 2008by Yoshio Mimura, Kobe, Japan
4573
85k + 1649k + 4097k + 4573k are squares for k = 1,2,3 (1022, 63582, 4109582).
Page of Squares : First Upload June 14, 2011 ; Last Revised June 14, 2011by Yoshio Mimura, Kobe, Japan
4575
45752 = 1053 + 1303 + 2603.
Page of Squares : First Upload September 1, 2008 ; Last Revised September 1, 2008by Yoshio Mimura, Kobe, Japan
4577
45772 = 933 + 1253 + 2633.
Page of Squares : First Upload September 1, 2008 ; Last Revised September 1, 2008by Yoshio Mimura, Kobe, Japan
4578
45782± 5 are primes.
45782 = 13 + 2103 + 2273.
45782 = 20958084, a zigzag square.
2793k + 4578k + 13062k + 15288k are squares for k = 1,2,3 (1892, 208112, 24329972).
Page of Squares : First Upload September 18, 2007 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
4579
45792 = 20967241, a zigzag square.
Page of Squares : First Upload September 18, 2007 ; Last Revised September 18, 2007by Yoshio Mimura, Kobe, Japan
4584
45842 = 823 + 923 + 2703 = 104 + 504 + 504 + 544.
Page of Squares : First Upload September 1, 2008 ; Last Revised September 1, 2008by Yoshio Mimura, Kobe, Japan
4588
45882 = (12 + 3)(112 + 3)(2062 + 3).
Page of Squares : First Upload December 28, 2013 ; Last Revised December 28, 2013by Yoshio Mimura, Kobe, Japan
4589
45894 = 443478153684241, and 442 + 32 + 472 + 82 + 152 + 32 + 62 + 82 + 42 + 22 + 42 + 12 = 4589.
Page of Squares : First Upload December 1, 2008 ; Last Revised December 1, 2008by Yoshio Mimura, Kobe, Japan
4590
45902 = (32 + 9)(92 + 9)(1142 + 9) = (52 + 9)(62 + 9)(92 + 9)(122 + 9) = (92 + 9)(122 + 9)(392 + 9).
A 4x4 perfect magic square consisting of squares with the constant 4590.
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Page of Squares : First Upload September 18, 2007 ; Last Revised December 28, 2013
by Yoshio Mimura, Kobe, Japan
4591
45912 = 125 + 145 + 155 + 255 + 255.
Page of Squares : First Upload September 1, 2008 ; Last Revised September 1, 2008by Yoshio Mimura, Kobe, Japan
4598
45982 = 933 + 1743 + 2473 = 993 + 1213 + 2643.
Page of Squares : First Upload September 1, 2008 ; Last Revised September 1, 2008by Yoshio Mimura, Kobe, Japan
4599
45992 = 33 + 933 + 2733.
45992 = (134 + 135 + 136 + ... + 154)2 + (155 + 156 + 157 + ... + 175)2.
Page of Squares : First Upload September 18, 2007 ; Last Revised September 1, 2008by Yoshio Mimura, Kobe, Japan