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9700 - 9799

9700

97002 = 404 + 604 + 604 + 904.

97002 = 31 x 32 + 32 x 33 + 33 x 34 + ... + 655 x 656.

510k + 690k + 1330k + 9570k are squares for k = 1,2,3 (1102, 97002, 9377002).

Page of Squares : First Upload October 14, 2008 ; Last Revised July 18, 2011
by Yoshio Mimura, Kobe, Japan

9701

97012 = 94109401, and 92 + 42 + 12 + 02 + 92 + 42 + 02 + 12 = 142.

Page of Squares : First Upload October 14, 2008 ; Last Revised October 14, 2008
by Yoshio Mimura, Kobe, Japan

9702

97022 = 114 + 594 + 794 + 814.

Page of Squares : First Upload October 14, 2008 ; Last Revised October 14, 2008
by Yoshio Mimura, Kobe, Japan

9703

97032 = 433 + 2913 + 4113.

The square root of 9703 is 98.5038...., and 98 = 52 + 02 + 32 + 82.

Page of Squares : First Upload October 14, 2008 ; Last Revised October 14, 2008
by Yoshio Mimura, Kobe, Japan

9704

97042 = 94167616, and 92 + 42 + 12 + 62 + 72 + 62 + 12 + 62 = 162.

Page of Squares : First Upload October 14, 2008 ; Last Revised October 14, 2008
by Yoshio Mimura, Kobe, Japan

9705

97052 = 94187025, a square with different digits.

Page of Squares : First Upload October 14, 2008 ; Last Revised October 14, 2008
by Yoshio Mimura, Kobe, Japan

9706

97062± 3 are primes.

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

9707

97075 = 86183702586115165307 :
82 + 62 + 182 + 372 + 02 + 22 + 582 + 62 + 12 + 152 + 12 + 652 + 32 + 02 + 72 = 9707.

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

9708

97082 = S2(215) + S2(648), where S2(n) = 12 + 22 + 32 + 42 + ... + n2.

Page of Squares : First Upload October 14, 2008 ; Last Revised October 14, 2008
by Yoshio Mimura, Kobe, Japan

9709

97092 = 94264681, and 94 * 26 * 4 - 68 + 1 = 9709.

97095 = 86272524285864367549 :
82 + 622 + 72 + 252 + 242 + 22 + 82 + 52 + 82 + 62 + 42 + 362 + 72 + 542 + 92 = 9709.

Page of Squares : First Upload October 14, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

9710

97102 = 923 + 1213 + 4513.

Page of Squares : First Upload October 14, 2008 ; Last Revised October 14, 2008
by Yoshio Mimura, Kobe, Japan

9712

97122± 3 are primes.

97122 = 244 + 444 + 484 + 964.

Page of Squares : First Upload October 14, 2008 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

9715

97152 = 94381225 appears in the decimal expressions of e:
  e = 2.71828•••94381225••• (from the 30781st digit)
  (94381225 is the sixth 8-digit square in the expression of e.)

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

9716

97162 = 383 + 1263 + 4523.

Page of Squares : First Upload October 14, 2008 ; Last Revised October 14, 2008
by Yoshio Mimura, Kobe, Japan

9717

97175 = 86628543710163888357 :
82 + 662 + 282 + 52 + 42 + 372 + 12 + 02 + 162 + 382 + 82 + 82 + 352 + 72 = 9717.

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

9720

1172 + 9720 = 1532, 1172 - 9720 = 632.

Page of Squares : First Upload October 14, 2008 ; Last Revised August 9, 2011
by Yoshio Mimura, Kobe, Japan

9721

97212 = 94497841, and 92 + 42 + 42 + 92 + 72 + 82 + 42 + 12 = 182.

97215 = 86806993631541312601 :
82 + 62 + 802 + 62 + 92 + 92 + 32 + 62 + 32 + 12 + 542 + 12 + 32 + 12 + 22 + 62 + 02 + 12 = 9721.

Page of Squares : First Upload October 14, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

9722

97222 = 94517284, a zigzag square.

97222 = 94517284, and 92 + 42 + 52 + 12 + 72 + 22 + 82 + 42 = 162.

Page of Squares : First Upload October 14, 2008 ; Last Revised October 14, 2008
by Yoshio Mimura, Kobe, Japan

9723

97232± 2 are primes.

1 / 9723 = 0.00010284891494, 102 + 22 + 842 + 82 + 92 + 12 + 492 + 42 = 9723.

Page of Squares : First Upload October 14, 2008 ; Last Revised January 11, 2014
by Yoshio Mimura, Kobe, Japan

9724

1326k + 2730k + 5226k + 7618k are squares for k = 1,2,3 (1302, 97242, 7794282).

Page of Squares : First Upload July 18, 2011 ; Last Revised July 18, 2011
by Yoshio Mimura, Kobe, Japan

9727

97272 = 94614529, and 9 * 4 * 6 * 1 * 45 - 2 + 9 = 9727.

97275 = 87075219795193937407 :
82 + 72 + 02 + 752 + 22 + 192 + 72 + 92 + 52 + 192 + 32 + 92 + 372 + 402 + 72 = 9727.

Page of Squares : First Upload October 14, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

9728

97282 = 383 + 3463 + 3763.

Page of Squares : First Upload October 14, 2008 ; Last Revised October 14, 2008
by Yoshio Mimura, Kobe, Japan

9729

97292± 2 are primes.

97295 = 87164775706363739649 :
82 + 72 + 162 + 472 + 72 + 52 + 72 + 02 + 632 + 62 + 372 + 392 + 62 + 42 + 92 = 9729.

Page of Squares : First Upload December 8, 2008 ; Last Revised January 11, 2014
by Yoshio Mimura, Kobe, Japan

9733

1 / 9733 = 0.0001027432446316, 102 + 22 + 742 + 322 + 42 + 462 + 312 + 62 = 9733.

Page of Squares : First Upload October 14, 2008 ; Last Revised October 14, 2008
by Yoshio Mimura, Kobe, Japan

9736

9736 = (12 + 22 + 32 + ... + 6082) / (12 + 22 + 32 + ... + 282).

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

9738

97382 = 94828644, and 9482 - 8 + 6 * 44 = 9738.

Loop of length 56 by the function f(N) = ... + c2 + b2 + a2 where N = ... + 1002c + 100b + a:
9738 - 10853 - 2874 - 6260 - ... - 8136 - 7857 - 9333 - 9738
(Note f(9738) = 972 + 382 = 10853,   f(10853) = 12 + 082 + 532 = 2874, etc. See 41)

Page of Squares : First Upload October 14, 2008 ; Last Revised October 14, 2008
by Yoshio Mimura, Kobe, Japan

9739

97392 = 94848121, a zigzag square.

Page of Squares : First Upload October 14, 2008 ; Last Revised October 14, 2008
by Yoshio Mimura, Kobe, Japan

9742

97422 = 2933 + 3183 + 3353.

97422 = 94906564, zigzag aquare.

Page of Squares : First Upload October 14, 2008 ; Last Revised October 14, 2008
by Yoshio Mimura, Kobe, Japan

9744

97442 = 164 + 604 + 804 + 804.

97442 = 94945536, and 92 + 42 + 92 + 42 + 52 + 52 + 32 + 62 = 172.

97445 = 87838796432853172224 :
82 + 72 + 82 + 32 + 872 + 92 + 62 + 42 + 32 + 282 + 52 + 312 + 72 + 22 + 22 + 22 + 42
= 872 + 82 + 32 + 82 + 72 + 92 + 62 + 42 + 32 + 282 + 52 + 312 + 72 + 22 + 22 + 22 + 42 = 9744.

Page of Squares : First Upload October 14, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

9745

12 + 42 + 72 + ... + (3x + 1)2 + ... + 97452 = 3207392.

97452 = 94965025, and 9 * 4 * 9 * 6 * 5 + 0 + 25 = 9745.

Page of Squares : First Upload October 14, 2008 ; Last Revised October 14, 2008
by Yoshio Mimura, Kobe, Japan

9746

97464 = 9022058279754256, and
92 + 02 + 22 + 22 + 02 + 52 + 82 + 22 + 72 + 972 + 52 + 42 + 22 + 52 + 62 = 9746.

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

9747

97472 = 573 + 4563.

A cubic polynomial :
(X + 28202)(X + 42402)(X + 97472) = X3 + 109972X2 + 510531002X + 1165429296002.

Page of Squares : First Upload October 14, 2008 ; Last Revised October 14, 2008
by Yoshio Mimura, Kobe, Japan

9748

97482 = 583 + 1703 + 4483.

Page of Squares : First Upload October 14, 2008 ; Last Revised October 14, 2008
by Yoshio Mimura, Kobe, Japan

9750

97502 = (12 + 9)(22 + 9)(42 + 9)(1712 + 9) = (12 + 9)(42 + 9)(112 + 9)(542 + 9)
= (42 + 9)(112 + 9)(1712 + 9).

97502 = 2003 + 3253 + 3753.

97502 = 95062500, 9 and 5062500 = 22502.

Page of Squares : First Upload October 14, 2008 ; Last Revised January 11, 2014
by Yoshio Mimura, Kobe, Japan

9754

The square root of 9754 is 98.7623...., and 98 = 72 + 62 + 22 + 32.

97545 = 88290455272414981024 :
82 + 82 + 292 + 02 + 42 + 52 + 52 + 272 + 242 + 142 + 92 + 812 + 02 + 242 = 9754.

Page of Squares : First Upload October 14, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

9756

97562 = 95179536, a square with odd digits except the last digit 6.

The square root of 9756 is 98.77...., and 98 = 72 + 72.

97562 = (13 + 14 + 15 + ... + 36)2 + (37 + 38 + 39 + ... + 60)2 + (61 + 62 + 63 + ... + 84)2 + ... + (205 + 206 + 207 + ... + 228)2.

Page of Squares : First Upload October 14, 2008 ; Last Revised August 24, 2013
by Yoshio Mimura, Kobe, Japan

9757

The square root of 9757 is 98.77...., and 98 = 72 + 72.

1 / 9757 = 0.00010249051962693, 102 + 242 + 92 + 052 + 192 + 622 + 692 + 32 = 9757.

1 / N = 0.0001024...., and 1024 = 322, for N = 9757, 9758,..., 9765.

97573 = 928857121093, and 92 + 282 + 82 + 52 + 72 + 12 + 22 + 102 + 932 = 9757.

Page of Squares : First Upload October 14, 2008 ; Last Revised December 1, 2008
by Yoshio Mimura, Kobe, Japan

9758

97582 = 95218564, and 9 * 5 * 218 - 56 + 4 = 9758.

Page of Squares : First Upload October 14, 2008 ; Last Revised October 14, 2008
by Yoshio Mimura, Kobe, Japan

9759

97592± 2 are primes.

Page of Squares : First Upload January 11, 2014 ; Last Revised January 11, 2014
by Yoshio Mimura, Kobe, Japan

9760

97605 = 88562341091737600000 :
82 + 852 + 62 + 232 + 412 + 02 + 92 + 12 + 72 + 32 + 72 + 62 + 02 + 02 + 02 + 02 + 02 = 9760.

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

9761

97612 = 1583 + 2663 + 4173.

Page of Squares : First Upload October 14, 2008 ; Last Revised October 14, 2008
by Yoshio Mimura, Kobe, Japan

9763

1 / 9763 = 0.00010242753252074, 102 + 22 + 42 + 272 + 532 + 252 + 22 + 0742 = 9763.

Page of Squares : First Upload October 14, 2008 ; Last Revised October 14, 2008
by Yoshio Mimura, Kobe, Japan

9764

97645 = 88743970114138317824 :
82 + 82 + 72 + 42 + 392 + 72 + 02 + 12 + 12 + 42 + 132 + 82 + 312 + 72 + 822 + 42 = 9764.

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

9765

97652 = 2423 + 4333 = 493 + 3383 + 3843.

97652 = 95355225, and 9535 + 5 + 225 = 9765.

97655 = 88789423898328103125 :
82 + 82 + 72 + 82 + 92 + 42 + 22 + 32 + 892 + 82 + 32 + 282 + 12 + 02 + 32 + 12 + 252
= 82 + 82 + 72 + 892 + 42 + 22 + 32 + 82 + 92 + 82 + 32 + 282 + 12 + 02 + 32 + 12 + 252 = 9765.

Page of Squares : First Upload October 14, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

9766

97662 = 95374756, and 9537 + 47 * 5 - 6 = 9766.

Page of Squares : First Upload October 14, 2008 ; Last Revised October 14, 2008
by Yoshio Mimura, Kobe, Japan

9767

97672 = 95394289, and 92 + 52 + 32 + 92 + 42 + 22 + 82 + 92 = 192.

Page of Squares : First Upload October 14, 2008 ; Last Revised October 14, 2008
by Yoshio Mimura, Kobe, Japan

9768

97682 = 363 + 1763 + 4483 = 493 + 3593 + 3663.

The integral triangle of sides 113, 1874080, 1874129 has square area 97682.

Page of Squares : First Upload October 14, 2008 ; Last Revised October 21, 2011
by Yoshio Mimura, Kobe, Japan

9770

The square root of 9770 is 98.8433...., and 98 = 82 + 42 + 32 + 32.

Page of Squares : First Upload October 14, 2008 ; Last Revised October 14, 2008
by Yoshio Mimura, Kobe, Japan

9772

The square root of 9772 is 98.853, and 98 = 82 + 52 + 32.

Page of Squares : First Upload October 14, 2008 ; Last Revised October 14, 2008
by Yoshio Mimura, Kobe, Japan

9773

97732 = 1513 + 2053 + 4373.

Page of Squares : First Upload October 14, 2008 ; Last Revised October 14, 2008
by Yoshio Mimura, Kobe, Japan

9774

97745 = 89199346672309542624 :
82 + 92 + 192 + 92 + 342 + 662 + 72 + 22 + 32 + 02 + 92 + 542 + 22 + 62 + 242 = 9774.

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

9777

97772 = 3133 + 3183 + 3203.

97772 = 95589729, and 9 * 5 - 5 + 8 + 9729 = 9777.

Page of Squares : First Upload October 14, 2008 ; Last Revised October 14, 2008
by Yoshio Mimura, Kobe, Japan

9778

97782 = 95609284, a zigzag square.

Page of Squares : First Upload October 14, 2008 ; Last Revised October 14, 2008
by Yoshio Mimura, Kobe, Japan

9779

97792 = 1643 + 1763 + 4413.

Page of Squares : First Upload October 14, 2008 ; Last Revised October 14, 2008
by Yoshio Mimura, Kobe, Japan

9781

97814 = 9152358761897521, and
92 + 12 + 52 + 22 + 32 + 582 + 72 + 62 + 12 + 82 + 92 + 752 + 212 = 9781.

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

9784

The square root of 9784 is 98.914...., and 98 = 92 + 12 + 42.

Page of Squares : First Upload October 14, 2008 ; Last Revised October 14, 2008
by Yoshio Mimura, Kobe, Japan

9785

969k + 5016k + 5092k + 6612k are squares for k = 1,2,3 (1332, 97852, 7404112).

Page of Squares : First Upload July 18, 2011 ; Last Revised July 18, 2011
by Yoshio Mimura, Kobe, Japan

9786

97862 = 95765796, and 95 * 7 * 6 + 5796 = 9786.

Page of Squares : First Upload October 14, 2008 ; Last Revised October 14, 2008
by Yoshio Mimura, Kobe, Japan

9789

97892 = 95824521, and 9582 + 4 * 52 - 1 = 9789.

Page of Squares : First Upload October 14, 2008 ; Last Revised October 14, 2008
by Yoshio Mimura, Kobe, Japan

9791

97912 = 95863681, and 9586 + 3 * 68 + 1 = 9791.

Page of Squares : First Upload October 14, 2008 ; Last Revised October 14, 2008
by Yoshio Mimura, Kobe, Japan

9792

97922± 5 are primes.

97922 = (172 - 1)(5772 - 1) = (22 - 1)(52 - 1)(332 - 1)(352 - 1).

97922 = 163 + 2883 + 4163 = 164 + 324 + 564 + 964 = 244 + 484 + 484 + 964.

Komachi equation: 97922 = 12 / 22 * 342 * 562 / 72 * 82 * 92.

Page of Squares : First Upload October 14, 2008 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

9794

97942 = 95922436, and 92 + 52 + 92 + 22 + 22 + 42 + 32 + 62 = 162.

Page of Squares : First Upload October 14, 2008 ; Last Revised October 14, 2008
by Yoshio Mimura, Kobe, Japan

9799

The sum of the squares of divisors of 9799 is a square, 98022.

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