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.
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, 2014by 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, 2014by 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, 2008by 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, 2008by 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.
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, 2014by 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, 2008by 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, 2008by 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.
by Yoshio Mimura, Kobe, Japan
9820
98202 = 2653 + 3163 + 3593.
Page of Squares : First Upload October 20, 2008 ; Last Revised October 20, 2008by Yoshio Mimura, Kobe, Japan
9822
98222 = 623 + 3373 + 3873.
Page of Squares : First Upload October 20, 2008 ; Last Revised October 20, 2008by Yoshio Mimura, Kobe, Japan
9823
98234 = 9310576572186241, and
92 + 32 + 12 + 02 + 52 + 762 + 572 + 22 + 12 + 82 + 62 + 242 + 12 = 9823.
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, 2008by 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, 2008by 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.
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.
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, 2013by Yoshio Mimura, Kobe, Japan
9834
98342 = 43 + 173 + 4593.
Page of Squares : First Upload October 20, 2008 ; Last Revised October 20, 2008by Yoshio Mimura, Kobe, Japan
9836
98362 = 9562 + 9572 + 9582 + 9592 + 9602 + ... + 10512.
Page of Squares : First Upload October 20, 2008 ; Last Revised October 20, 2008by 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.
by Yoshio Mimura, Kobe, Japan
9840
98402 = 543 + 2713 + 4253.
Page of Squares : First Upload October 20, 2008 ; Last Revised October 20, 2008by 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, 2008by 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, 2014by 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.
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, 2008by 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.
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, 2008by Yoshio Mimura, Kobe, Japan
9848
98484 = 9405722461474816, and
942 + 02 + 52 + 72 + 222 + 42 + 62 + 12 + 42 + 72 + 42 + 82 + 162 = 9848.
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.
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, 2014by 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, 2008by 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, 2008by 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, 2011by 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, 2014by 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).
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.
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.
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, 2013by 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, 2011by Yoshio Mimura, Kobe, Japan
9872
98722 = 1603 + 1803 + 4443 = 1943 + 2203 + 4303.
Page of Squares : First Upload October 20, 2008 ; Last Revised October 20, 2008by Yoshio Mimura, Kobe, Japan
9873
98732 = 2243 + 2893 + 3963.
Page of Squares : First Upload October 20, 2008 ; Last Revised October 20, 2008by 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, 2013by 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, 2014by Yoshio Mimura, Kobe, Japan
9880
1 + 2 + 3 + 4 + 5 + ... + 9800 = 69302.
Page of Squares : First Upload November 25, 2008 ; Last Revised November 25, 2008by 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.
by Yoshio Mimura, Kobe, Japan
9882
98822 = 274 + 274 + 274 + 994.
Page of Squares : First Upload October 20, 2008 ; Last Revised October 20, 2008by Yoshio Mimura, Kobe, Japan
9885
98852 = 173 + 3103 + 4083.
Page of Squares : First Upload October 20, 2008 ; Last Revised October 20, 2008by Yoshio Mimura, Kobe, Japan
9887
98872 = 324 + 324 + 434 + 984.
Page of Squares : First Upload October 20, 2008 ; Last Revised October 20, 2008by 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, 2008by 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, 2011by 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.
by Yoshio Mimura, Kobe, Japan
9894
98945 = 94811175283002544224 :
92 + 42 + 812 + 12 + 172 + 52 + 282 + 302 + 02 + 252 + 42 + 42 + 22 + 242 = 9894.
by Yoshio Mimura, Kobe, Japan
9897
98972 = 514 + 564 + 684 + 884.
Page of Squares : First Upload October 20, 2008 ; Last Revised October 20, 2008by Yoshio Mimura, Kobe, Japan