7500
75002 = 56250000, and
5 * 6 / 2 * 500 + 0 + 0 = 5 * 6 / 2 * 500 + 0 * 0 = 5 * 6 * 250 + 0 + 0 + 0
= 5 * 6 * 250 + 0 + 0 * 0 = 5 * 6 * 250 + 0 * 0 + 0 = 5 * 6 * 250 + 0 * 0 * 0 = 7500.
by Yoshio Mimura, Kobe, Japan
7501
7501 = 702 + 512.
75012 = (103 + 104)2 + (105 + 106)2 + (107 + 108)2 + ... + (439 + 440)2.
Page of Squares : First Upload May 12, 2008 ; Last Revised May 12, 2008by Yoshio Mimura, Kobe, Japan
7502
75022 = 1673 + 2693 + 3183.
Page of Squares : First Upload May 12, 2008 ; Last Revised May 12, 2008by Yoshio Mimura, Kobe, Japan
7503
75032 = 23 + 2893 + 3183.
75032 + 75042 + 75052 + ... + 75642 = 75652 + 73662 + 73672 + ... + 76252.
Page of Squares : First Upload May 12, 2008 ; Last Revised September 16, 2011by Yoshio Mimura, Kobe, Japan
7509
(75092 + 3) = (22 + 3)(42 + 3)(52 + 3)(102 + 3)(122 + 3).
Page of Squares : First Upload May 12, 2008 ; Last Revised May 12, 2008by Yoshio Mimura, Kobe, Japan
7512
The square root of 7512 is 86.671...., and 86 = 62 + 72 + 12.
Page of Squares : First Upload May 12, 2008 ; Last Revised May 12, 2008by Yoshio Mimura, Kobe, Japan
7513
75135 = 23936847018133908793 :
232 + 92 + 362 + 82 + 42 + 702 + 182 + 12 + 32 + 32 + 92 + 02 + 82 + 72 + 92 + 32 = 7513.
by Yoshio Mimura, Kobe, Japan
7514
5330k + 6682k + 7514k + 13598k are squares for k = 1,2,3 (1822, 177322, 18407482).
Page of Squares : First Upload July 8, 2011 ; Last Revised July 8, 2011by Yoshio Mimura, Kobe, Japan
7515
75152 = 56475225, and 5 - 6 - 4 + 752 * 2 * 5 = 7515.
Page of Squares : First Upload May 12, 2008 ; Last Revised May 12, 2008by Yoshio Mimura, Kobe, Japan
7518
75185 = 24016604534438489568 :
242 + 02 + 12 + 62 + 62 + 02 + 42 + 52 + 32 + 442 + 32 + 82 + 42 + 82 + 92 + 52 + 682 = 7518.
by Yoshio Mimura, Kobe, Japan
7520
75202 = 1853 + 2483 + 3273.
Page of Squares : First Upload May 12, 2008 ; Last Revised May 12, 2008by Yoshio Mimura, Kobe, Japan
7524
75242 = (12 + 8)(22 + 8)(52 + 8)(1262 + 8) = (12 + 8)(62 + 8)(72 + 8)(502 + 8)
= (22 + 8)(172 + 8)(1262 + 8) = (22 + 8)(262 + 8)(832 + 8) = (22 + 8)(52 + 8)(72 + 8)(502 + 8)
= (52 + 8)(102 + 8)(1262 + 8) = (52 + 8)(262 + 8)(502 + 8) = (52 + 8)(62 + 8)(72 + 8)(262 + 8)
= (72 + 8)(262 + 8)(382 + 8).
by Yoshio Mimura, Kobe, Japan
7525
75252 = 56625625, a square consisting of just 3 kinds of digits.
75252 = 56625625, and 5 * 6 + 625 * 6 * 2 - 5 = 7525.
Page of Squares : First Upload May 12, 2008 ; Last Revised May 12, 2008by Yoshio Mimura, Kobe, Japan
7528
Loop of length 56 by the function f(N) = ... + c2 + b2 + a2 where N = ... + 1002c + 100b + a:
7528 - 6409 - 4177 - 7610 - ... - 7785 - 13154 - 3878 - 7528
(Note f(7528) = 752 + 282 = 6409, f(6409) = 642 + 092 = 4177, etc. See 41)
by Yoshio Mimura, Kobe, Japan
7531
75314 = 3216700232153521,
and 32 + 212 + 62 + 702 + 02 + 22 + 32 + 212 + 52 + 352 + 212 = 7531.
by Yoshio Mimura, Kobe, Japan
7532
75322 = 56731024, a square consisting of different digits.
1 / 7532 = 0.000132766861, 12 + 32 + 22 + 72 + 62 + 62 + 862 + 12 = 7532.
75325 = 24241057221355154432 :
22 + 422 + 42 + 102 + 572 + 22 + 212 + 32 + 52 + 52 + 12 + 52 + 42 + 432 + 22 = 7532.
by Yoshio Mimura, Kobe, Japan
7533
75332 = 56746089, and 56 + 7460 + 8 + 9 = 7533.
75332 = 1893 + 1893 + 3513.
Page of Squares : First Upload May 12, 2008 ; Last Revised May 12, 2008by Yoshio Mimura, Kobe, Japan
7536
75362 = 25 + 165 + 225 + 225 + 345.
Page of Squares : First Upload May 12, 2008 ; Last Revised May 12, 2008by Yoshio Mimura, Kobe, Japan
7537
75375 = 24321624343912881457 :
22 + 42 + 322 + 162 + 242 + 32 + 42 + 392 + 12 + 282 + 82 + 12 + 42 + 572
= 242 + 322 + 162 + 22 + 42 + 32 + 42 + 392 + 12 + 282 + 82 + 12 + 42 + 572 = 7537.
by Yoshio Mimura, Kobe, Japan
7540
75402 = (12 + 1)(32 + 1)(172 + 1)(992 + 1) = (12 + 1)(32 + 1)(52 + 1)(82 + 1)(412 + 1)
= (12 + 4)(242 + 4)(1402 + 4) = (12 + 4)(42 + 4)(52 + 4)(1402 + 4)
= (32 + 4)(52 + 4)(162 + 4)(242 + 4).
by Yoshio Mimura, Kobe, Japan
7543
75432 = 56896849, 5 + 689 + 6849 = 7543.
75435 = 24418587507289545943 :
22 + 42 + 42 + 182 + 582 + 72 + 52 + 02 + 72 + 22 + 82 + 92 + 52 + 42 + 592 + 42 + 32 = 7543.
by Yoshio Mimura, Kobe, Japan
7544
75445 = 24434778056718516224 :
242 + 42 + 32 + 472 + 72 + 82 + 02 + 52 + 62 + 72 + 12 + 82 + 52 + 12 + 622 + 242 = 7544.
by Yoshio Mimura, Kobe, Japan
7546
75462 = 113 + 2733 + 3323.
Page of Squares : First Upload May 12, 2008 ; Last Revised May 12, 2008by Yoshio Mimura, Kobe, Japan
7548
75482 = 56972304, a square consisting of different digits.
Page of Squares : First Upload May 12, 2008 ; Last Revised May 12, 2008by Yoshio Mimura, Kobe, Japan
7549
75492 = 56987401, a square consisting of different digits.
Page of Squares : First Upload May 12, 2008 ; Last Revised May 12, 2008by Yoshio Mimura, Kobe, Japan
7552
75522 = 57032704, a zigzag square.
75522 = 1303 + 2603 + 3343 = 1483 + 2293 + 3473.
75525 = 24564611866565804032 :
22 + 452 + 62 + 42 + 62 + 12 + 182 + 62 + 62 + 52 + 62 + 582 + 02 + 402 + 32 + 22 = 7552.
by Yoshio Mimura, Kobe, Japan
7553
7553 = (12 + 22 + 32 + ... + 5392) / (12 + 22 + 32 + ... + 272).
Page of Squares : First Upload November 25, 2008 ; Last Revised November 25, 2008by Yoshio Mimura, Kobe, Japan
7554
75542± 5 are primes.
75542 = 57062916, a zigzag square.
75542 = 1773 + 2483 + 3313.
Page of Squares : First Upload May 12, 2008 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
7555
75555 = 24613441585839221875 :
242 + 62 + 12 + 32 + 42 + 42 + 152 + 82 + 52 + 82 + 32 + 92 + 222 + 182 + 752 = 7555.
by Yoshio Mimura, Kobe, Japan
7557
75572 = 57108249, a square consisting of different digits.
75572 = 1333 + 1833 + 3653.
Page of Squares : First Upload May 12, 2008 ; Last Revised May 12, 2008by Yoshio Mimura, Kobe, Japan
7558
75585 = 24662348925524956768 :
242 + 62 + 62 + 232 + 482 + 92 + 22 + 52 + 52 + 242 + 92 + 562 + 72 + 62 + 82 = 7558.
by Yoshio Mimura, Kobe, Japan
7560
75602 = (22 - 1)(42 - 1)(52 - 1)(82 - 1)(292 - 1) = (22 - 1)(42 - 1)(82 - 1)(112 - 1)(132 - 1)
= (22 - 1)(52 - 1)(62 - 1)(82 - 1)(192 - 1) = (22 - 1)(82 - 1)(192 - 1)(292 - 1)
= (32 - 1)(112 - 1)(2442 - 1) = (32 - 1)(82 - 1)(132 - 1)(262 - 1) = (312 - 1)(2442 - 1)
= (42 - 1)(82 - 1)(132 - 1)(192 - 1) = (62 - 1)(82 - 1)(1612 - 1).
1112 + 7560 = 1412, 1112 - 7560 = 692,
872 + 7560 = 1232, 872 - 7560 = 32.
75602 = 543 + 1443 + 3783 = 1323 + 2243 + 3523 = 1683 + 2643 + 3243.
Komachi equations:
75602 = 92 * 82 * 72 / 62 * 542 / 32 / 22 * 102 = 982 / 72 * 62 * 542 / 32 / 22 * 102
= 982 / 72 / 62 * 542 * 32 * 22 * 102.
by Yoshio Mimura, Kobe, Japan
7561
1 / 7561 = 0.00013225...., and 13225 = 1152.
Page of Squares : First Upload May 12, 2008 ; Last Revised May 12, 2008by Yoshio Mimura, Kobe, Japan
7562
75624 = 3269992014616336,
and 322 + 692 + 92 + 92 + 202 + 12 + 42 + 62 + 12 + 62 + 332 + 62 = 7562.
by Yoshio Mimura, Kobe, Japan
7563
75632 = 57198969, a zigzag square.
Page of Squares : First Upload May 12, 2008 ; Last Revised May 12, 2008by Yoshio Mimura, Kobe, Japan
7564
75642 = 57214096, a square consisting of different digits.
75642 = 57214096, 5 - 7 + 21 * 40 * 9 + 6 = 7564.
75642 = 7242 + 7252 + 7262 + 7272 + 7282 + 7292 + ... + 8192.
Page of Squares : First Upload May 12, 2008 ; Last Revised May 12, 2008by Yoshio Mimura, Kobe, Japan
7565
75652 = 57229225, and 52 + 72 + 22 + 22 + 92 + 22 + 22 + 52 = 142.
Page of Squares : First Upload May 12, 2008 ; Last Revised May 12, 2008by Yoshio Mimura, Kobe, Japan
7566
75662 = (452 + 3)(1682 + 3) = (62 + 3)(72 + 3)(1682 + 3).
Page of Squares : First Upload January 11, 2014 ; Last Revised January 11, 2014by Yoshio Mimura, Kobe, Japan
7568
75682 = 57274624, a zigzag square.
75682± 3 are primes.
75682 = (12 + 7)(22 + 7)(62 + 7)(1232 + 7) = (22 + 7)(62 + 7)(92 + 7)(372 + 7)
= (62 + 7)(312 + 7)(372 + 7) = (62 + 7)(92 + 7)(1232 + 7).
75682 = 2043 + 2883 + 2923.
Page of Squares : First Upload May 12, 2008 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
7569
The square of 87.
75692± 2 are primes.
75692 = 873 + 1453 + 3773.
75695 = 24842341419143568849 :
22 + 482 + 42 + 22 + 342 + 12 + 42 + 12 + 92 + 142 + 352 + 62 + 82 + 82 + 492
= 22 + 482 + 42 + 22 + 342 + 142 + 12 + 92 + 12 + 42 + 352 + 62 + 82 + 82 + 492 = 7569.
by Yoshio Mimura, Kobe, Japan
7572
75722 = 57335184, and 5 + 7 + 3 * 35 * 18 * 4 = 7572.
Page of Squares : First Upload May 12, 2008 ; Last Revised May 12, 2008by Yoshio Mimura, Kobe, Japan
7573
75732 = 57350329, a zigzag square.
Page of Squares : First Upload May 12, 2008 ; Last Revised May 12, 2008by Yoshio Mimura, Kobe, Japan
7575
75752 = 57380625, a zigzag square.
75752 = 404 + 604 + 654 + 704.
Page of Squares : First Upload May 12, 2008 ; Last Revised May 12, 2008by Yoshio Mimura, Kobe, Japan
7576
75762 = 57395776, a square with odd digits except the last digit 6.
Page of Squares : First Upload August 24, 2013 ; Last Revised August 24, 2013by Yoshio Mimura, Kobe, Japan
7577
75772 = 57410929, 5 + 7410 + 9 * 2 * 9 = 7577.
Page of Squares : First Upload May 12, 2008 ; Last Revised May 12, 2008by Yoshio Mimura, Kobe, Japan
7582
75822 = 57486724, a zigzag square.
75822 = 34 + 74 + 214 + 874.
Page of Squares : First Upload May 12, 2008 ; Last Revised May 12, 2008by Yoshio Mimura, Kobe, Japan
7584
105 + 7584 = 3282, 105 - 7584 = 3042.
Page of Squares : First Upload August 5, 2011 ; Last Revised August 5, 2011by Yoshio Mimura, Kobe, Japan
7587
75872 = 57562569, 5 + 7562 + 5 + 6 + 9 = 7587.
75872 = 813 + 2463 + 3483 = 823 + 2333 + 3543 = 1233 + 2973 + 3093.
Page of Squares : First Upload May 12, 2008 ; Last Revised May 12, 2008by Yoshio Mimura, Kobe, Japan
7588
75882 = 57577744, a square consisting of just 3 kinds of digits.
1 / 7588 = 0.000131787032156, 132 + 12 + 782 + 72 + 02 + 322 + 152 + 62 = 7588,
1 / 7588 = 0.000131787032156, 132 + 12 + 782 + 72 + 0322 + 152 + 62 = 7588.
The square root of 7588 is 87.10912...., and 87 = 12 + 02 + 92 + 12 + 22.
75882 = 57577744, and 5 + 7577 + 7 - 4 / 4 = 7588.
75882 = 353 + 1783 + 3733.
75884 = 3315196604129536,
and 332 + 152 + 12 + 92 + 662 + 02 + 412 + 22 + 92 + 52 + 32 + 62 = 7588.
by Yoshio Mimura, Kobe, Japan
7589
1 / 7589 = 0.000131769...., and 131769 = 3632.
75892 = 57592921, and 5 + 7592 - 9 + 2 - 1 = 7589.
75893 = 437072677469, and 42 + 32 + 72 + 02 + 722 + 62 + 72 + 72 + 462 + 92 = 7589.
Page of Squares : First Upload May 12, 2008 ; Last Revised December 1, 2008by Yoshio Mimura, Kobe, Japan
7592
The square root of 7592 is 87.132083...., and 87 = 12 + 32 + 22 + 02 + 82 + 32.
Page of Squares : First Upload May 12, 2008 ; Last Revised May 12, 2008by Yoshio Mimura, Kobe, Japan
7596
1 / 7596 = 0.0001316482359136387572406529, and
13162 + 4822 + 35912 + 362 + 3872 + 572 + 2402 + 65292 = 75962.
by Yoshio Mimura, Kobe, Japan
7597
75972 = 1503 + 1603 + 3693.
Page of Squares : First Upload May 12, 2008 ; Last Revised May 12, 2008by Yoshio Mimura, Kobe, Japan
7598
75985 = 25321909138419807968 :
252 + 32 + 212 + 92 + 02 + 92 + 12 + 382 + 42 + 12 + 92 + 82 + 02 + 72 + 92 + 682 = 7598.
by Yoshio Mimura, Kobe, Japan
7599
The square root of 7599 is 87.1722432...., and 87 = 12 + 72 + 22 + 22 + 42 + 32 + 22.
Page of Squares : First Upload May 12, 2008 ; Last Revised May 12, 2008by Yoshio Mimura, Kobe, Japan