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9800 - 9899

9800

98002 = 2803 + 4203 = 283 + 2043 + 4443 = 704 + 704 + 704 + 704.

1 + 2 + 3 + ... + 9800 = 69302 and 98002 - 97992 + 97982 - ... - 12 = 69302.

Komachi equations:
98002 = 93 * 83 * 73 / 63 * 53 + 43 / 33 * 2103 = 983 / 73 * 63 * 53 + 43 / 33 * 2103.

Page of Squares : First Upload October 20, 2008 ; Last Revised November 29, 2010
by Yoshio Mimura, Kobe, Japan

9801

The square of 99.

9801 = (98 + 01)2.

98012± 2 are primes.

98012 = 1443 + 1773 + 4443 = 1983 + 2973 + 3963.

9801 = 992 and 1089 = 332.

98029801 = 99012.

Page of Squares : First Upload October 20, 2008 ; Last Revised January 11, 2014
by Yoshio Mimura, Kobe, Japan

9802

1 / 9802 = 0.00010201...., and 10201 = 1012.

98022 = 96079204, and 9607 - 9 + 204 = 9802.

98022 = (12 + 1)(702 + 1)(992 + 1) = (412 + 1)(2392 + 1).

98029801 = 99012.

98022 = (12 + 1)(702 + 1)(992 + 1) = (412 + 1)(2392 + 1).

Page of Squares : First Upload October 20, 2008 ; Last Revised January 11, 2014
by Yoshio Mimura, Kobe, Japan

9803

The square root of 9803 is 99.01010049...., and 99 = 02 + 12 + 02 + 12 + 02 + 02 + 42 + 92.

Page of Squares : First Upload October 20, 2008 ; Last Revised October 20, 2008
by Yoshio Mimura, Kobe, Japan

9805

98052 = 96138025, a square with different digits.

98052 = 96138025 with 961 = 312 and 38025 = 1952.

Page of Squares : First Upload October 20, 2008 ; Last Revised October 20, 2008
by Yoshio Mimura, Kobe, Japan

9807

98072 = 96177249, and 9 * 6 * 177 + 249 = 9807.

98074 = 9250063225208001, and
92 + 22 + 502 + 02 + 632 + 222 + 522 + 02 + 82 + 02 + 02 + 12 = 9807.

Page of Squares : First Upload October 20, 2008 ; Last Revised December 1, 2008
by Yoshio Mimura, Kobe, Japan

9810

98102 = (92 + 9)(102 + 9)(992 + 9).

98102 = 143 + 3373 + 3873.

Page of Squares : First Upload October 20, 2008 ; Last Revised January 11, 2014
by Yoshio Mimura, Kobe, Japan

9811

98112 = 2253 + 3223 + 3723.

98112 = 96255721, and 92 + 62 + 22 + 52 + 52 + 72 + 22 + 12 = 152.

Page of Squares : First Upload October 20, 2008 ; Last Revised October 20, 2008
by Yoshio Mimura, Kobe, Japan

9815

98152 = 96334225, and 96 * 3 * 34 - 2 + 25 = 9815.

Page of Squares : First Upload October 20, 2008 ; Last Revised October 20, 2008
by Yoshio Mimura, Kobe, Japan

9816

1 / 9816 = 0.0001018744906275, 12 + 0182 + 742 + 42 + 92 + 0622 + 72 + 52 = 9816.

98165 = 91132387596530712576 :
92 + 12 + 132 + 22 + 32 + 82 + 72 + 52 + 962 + 52 + 32 + 02 + 72 + 12 + 22 + 52 + 72 + 62 = 9816.

Page of Squares : First Upload October 20, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

9820

98202 = 2653 + 3163 + 3593.

Page of Squares : First Upload October 20, 2008 ; Last Revised October 20, 2008
by Yoshio Mimura, Kobe, Japan

9822

98222 = 623 + 3373 + 3873.

Page of Squares : First Upload October 20, 2008 ; Last Revised October 20, 2008
by Yoshio Mimura, Kobe, Japan

9823

98234 = 9310576572186241, and
92 + 32 + 12 + 02 + 52 + 762 + 572 + 22 + 12 + 82 + 62 + 242 + 12 = 9823.

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

9825

98252 = 1763 + 3243 + 3853 = 304 + 404 + 804 + 854.

Page of Squares : First Upload October 20, 2008 ; Last Revised October 20, 2008
by Yoshio Mimura, Kobe, Japan

9826

98262 = 176 + 176 + 176 + 176.

98262 = 96550276, and 92 + 62 + 52 + 52 + 02 + 22 + 72 + 62 = 162.

Page of Squares : First Upload October 20, 2008 ; Last Revised October 20, 2008
by Yoshio Mimura, Kobe, Japan

9827

98272 = 13 + 3063 + 4083.

98272 = 96569929, and 9656 + 9 + 9 * 2 * 9 = 9656 + 9 * 9 * 2 + 9 = 9827.

98275 = 91644156915288157907 :
92 + 12 + 62 + 42 + 42 + 12 + 52 + 62 + 92 + 12 + 522 + 82 + 812 + 52 + 72 + 92 + 02 + 72 = 9827.

Page of Squares : First Upload October 20, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

9830

98304 = 9337144315210000, and
932 + 32 + 72 + 12 + 42 + 42 + 312 + 52 + 22 + 102 + 02 + 02 + 02
92 + 12 + 72 + 82 + 412 + 22 + 862 + 182 + 52 + 142 + 32 + 02 + 02 + 02 + 02 + 02 = 9830.

Page of Squares : First Upload December 1, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

9833

98332 = 96687889, a square every digit of which is greater than 5.

Page of Squares : First Upload September 7, 2013 ; Last Revised September 7, 2013
by Yoshio Mimura, Kobe, Japan

9834

98342 = 43 + 173 + 4593.

Page of Squares : First Upload October 20, 2008 ; Last Revised October 20, 2008
by Yoshio Mimura, Kobe, Japan

9836

98362 = 9562 + 9572 + 9582 + 9592 + 9602 + ... + 10512.

Page of Squares : First Upload October 20, 2008 ; Last Revised October 20, 2008
by Yoshio Mimura, Kobe, Japan

9837

98375 = 92111394433524432957 :
92 + 212 + 112 + 32 + 92 + 42 + 42 + 332 + 522 + 442 + 32 + 22 + 92 + 572
= 92 + 212 + 112 + 32 + 92 + 442 + 332 + 522 + 42 + 42 + 32 + 22 + 92 + 572 = 9837.

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

9840

98402 = 543 + 2713 + 4253.

Page of Squares : First Upload October 20, 2008 ; Last Revised October 20, 2008
by Yoshio Mimura, Kobe, Japan

9841

98412 = 96845281, a zigzag square.

98412 = 96845281, and 9684 - 5 + 2 * 81 = 9841.

Page of Squares : First Upload October 20, 2008 ; Last Revised October 20, 2008
by Yoshio Mimura, Kobe, Japan

9842

98422 = (22 + 3)(42 + 3)(162 + 3)(532 + 3)

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

9843

1 / 9843 = 0.00010159504216, 102 + 152 + 952 + 02 + 42 + 212 + 62 = 9843,
1 / 9843 = 0.00010159504216, 102 + 152 + 952 + 042 + 212 + 62 = 9843.

Page of Squares : First Upload October 20, 2008 ; Last Revised October 20, 2008
by Yoshio Mimura, Kobe, Japan

9844

9844 = (12 + 22 + 32 + ... + 1602) / (12 + 22 + 32 + ... + 72).

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

9845

98455 = 92486554895565153125 :
92 + 22 + 42 + 82 + 62 + 52 + 52 + 42 + 82 + 952 + 52 + 62 + 52 + 152 + 32 + 122 + 52 = 9845.

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

9847

98472 = 403 + 3603 + 3693 = 164 + 644 + 674 + 884.

Page of Squares : First Upload October 20, 2008 ; Last Revised October 20, 2008
by Yoshio Mimura, Kobe, Japan

9848

98484 = 9405722461474816, and
942 + 02 + 52 + 72 + 222 + 42 + 62 + 12 + 42 + 72 + 42 + 82 + 162 = 9848.

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

9849

98492 = 493 + 3503 + 3783.

98495 = 92674592964777324249 :
92 + 22 + 672 + 452 + 92 + 22 + 92 + 62 + 42 + 72 + 72 + 72 + 322 + 422 + 42 + 92 = 9849.

Page of Squares : First Upload October 20, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

9850

98502 = (22 + 1)(32 + 1)(13932 + 1) = (72 + 1)(13932 + 1).

98502 = 997022500 with 9 = 32 and 7022500 = 26502.

98502 = (22 + 1)(32 + 1)(13932 + 1) = (72 + 1)(13932 + 1).

Page of Squares : First Upload October 20, 2008 ; Last Revised January 11, 2014
by Yoshio Mimura, Kobe, Japan

9852

The square root of 9852 is 99.257241...., and 99 = 22 + 52 + 72 + 22 + 42 + 12.

Page of Squares : First Upload October 20, 2008 ; Last Revised October 20, 2008
by Yoshio Mimura, Kobe, Japan

9854

98542 = 2343 + 2793 + 3973.

The square root of 9854 is 99.26731...., and 99 = 22 + 62 + 72 + 32 + 12.

Page of Squares : First Upload October 20, 2008 ; Last Revised October 20, 2008
by Yoshio Mimura, Kobe, Japan

9855

98552 = 683 + 3453 + 3823 = 1023 + 2493 + 4323 = 2703 + 3213 + 3543.

The sum of the squares of divisors of 9855 is a square, 106602.

Page of Squares : First Upload October 20, 2008 ; Last Revised November 1, 2011
by Yoshio Mimura, Kobe, Japan

9856

98562 = (12 + 7)(22 + 7)(32 + 7)(72 + 7)(352 + 7) = (12 + 7)(72 + 7)(132 + 7)(352 + 7)
= (132 + 7)(212 + 7)(352 + 7) = (22 + 7)(32 + 7)(212 + 7)(352 + 7)
= (22 + 7)(72 + 7)(112 + 7)(352 + 7) = (32 + 7)(72 + 7)(92 + 7)(352 + 7).

98562 = 283 + 1323 + 4563

Page of Squares : First Upload October 20, 2008 ; Last Revised January 11, 2014
by Yoshio Mimura, Kobe, Japan

9860

98602 = (12 + 1)(32 + 1)(42 + 1)(132 + 1)(412 + 1) = (52 + 4)(242 + 4)(762 + 4)
= (52 + 4)(82 + 4)(92 + 4)(242 + 4).

Page of Squares : First Upload November 2, 2013 ; Last Revised January 11, 2014
by Yoshio Mimura, Kobe, Japan

9863

1 / 9863 = 0.000101389029706, 102 + 132 + 82 + 92 + 02 + 22 + 972 + 062 = 9863,
1 / 9863 = 0.000101389029706, 102 + 132 + 82 + 92 + 022 + 972 + 02 + 62 = 9863,
1 / 9863 = 0.000101389029706, 102 + 132 + 82 + 92 + 022 + 972 + 062 = 9863.

Page of Squares : First Upload October 20, 2008 ; Last Revised October 20, 2008
by Yoshio Mimura, Kobe, Japan

9864

98642 = 643 + 2283 + 4403.

98644 = 9466997323862016, and
92 + 462 + 62 + 92 + 92 + 732 + 22 + 382 + 62 + 202 + 162 = 9864.

Page of Squares : First Upload October 20, 2008 ; Last Revised December 1, 2008
by Yoshio Mimura, Kobe, Japan

9866

98662 = 97337956, a square with odd digits except the last digit 6.

(98662 - 2) = (82 - 2)(92 - 2)(112 - 2)(132 - 2) = (22 - 2)(32 - 2)(92 - 2)(132 - 2)(232 - 2).

Page of Squares : First Upload October 20, 2008 ; Last Revised August 24, 2013
by Yoshio Mimura, Kobe, Japan

9870

4089k + 9870k + 15792k + 25474k are squares for k = 1,2,3 (2352, 318192, 46366912).

98702 + 98712 + 98722 + ... + 99402 = 99412 + 99422 + 99432 + ... + 100102.

Page of Squares : First Upload July 18, 2011 ; Last Revised September 20, 2011
by Yoshio Mimura, Kobe, Japan

9872

98722 = 1603 + 1803 + 4443 = 1943 + 2203 + 4303.

Page of Squares : First Upload October 20, 2008 ; Last Revised October 20, 2008
by Yoshio Mimura, Kobe, Japan

9873

98732 = 2243 + 2893 + 3963.

Page of Squares : First Upload October 20, 2008 ; Last Revised October 20, 2008
by Yoshio Mimura, Kobe, Japan

9876

98762 = 97535376, 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

9879

98792± 2 are primes.

The square root of 9879 is 99.393...., and 99 = 32 + 92 + 32.

Page of Squares : First Upload October 20, 2008 ; Last Revised January 11, 2014
by Yoshio Mimura, Kobe, Japan

9880

1 + 2 + 3 + 4 + 5 + ... + 9800 = 69302.

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

9881

98812 = 2173 + 3303 + 3723.

Loop of length 56 by the function f(N) = ... + c2 + b2 + a2 where N = ... + 1002c + 100b + a:
9881 - 16165 - 7947 - 8450 - ... - 7610 - 5876 - 9140 - 9881
(Note f(9881) = 982 + 812 = 16165,   f(16165) = 12 + 612 + 652 = 7947, etc. See 41)

98815 = 94189934843832513401 :
92 + 42 + 12 + 82 + 92 + 932 + 42 + 82 + 42 + 32 + 82 + 32 + 252 + 132 + 42 + 02 + 12 = 9881.

Page of Squares : First Upload October 20, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

9882

98822 = 274 + 274 + 274 + 994.

Page of Squares : First Upload October 20, 2008 ; Last Revised October 20, 2008
by Yoshio Mimura, Kobe, Japan

9885

98852 = 173 + 3103 + 4083.

Page of Squares : First Upload October 20, 2008 ; Last Revised October 20, 2008
by Yoshio Mimura, Kobe, Japan

9887

98872 = 324 + 324 + 434 + 984.

Page of Squares : First Upload October 20, 2008 ; Last Revised October 20, 2008
by Yoshio Mimura, Kobe, Japan

9888

98882 = 524 + 524 + 764 + 844.

98882 = 97772544, and 92 + 72 + 72 + 72 + 22 + 52 + 42 + 42 = 172.

Page of Squares : First Upload October 20, 2008 ; Last Revised October 20, 2008
by Yoshio Mimura, Kobe, Japan

9890

897k + 2806k + 9890k + 12328k are squares for k = 1,2,3 (1612, 160772, 16922712).

9890 = (12 + 22 + 32 + ... + 66002) / (12 + 22 + 32 + ... + 3072).

Page of Squares : First Upload November 25, 2008 ; Last Revised July 18, 2011
by Yoshio Mimura, Kobe, Japan

9891

98912± 2 are primes.

98912 = 443 + 2173 + 4443.

98915 = 94667522013521810451 :
942 + 62 + 62 + 72 + 52 + 22 + 202 + 12 + 32 + 52 + 22 + 182 + 102 + 42 + 52 + 12 = 9891.

Page of Squares : First Upload October 20, 2008 ; Last Revised January 11, 2014
by Yoshio Mimura, Kobe, Japan

9894

98945 = 94811175283002544224 :
92 + 42 + 812 + 12 + 172 + 52 + 282 + 302 + 02 + 252 + 42 + 42 + 22 + 242 = 9894.

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

9897

98972 = 514 + 564 + 684 + 884.

Page of Squares : First Upload October 20, 2008 ; Last Revised October 20, 2008
by Yoshio Mimura, Kobe, Japan