9900
730k + 3970k + 4190k + 8010k are squares for k = 1,2,3 (1302, 99002, 8065002).
The integral triangle of sides 7193, 27257, 28050 (or 1618, 168993, 170125) has square area 99002.
Page of Squares : First Upload July 18, 2011 ; Last Revised October 21, 2011by Yoshio Mimura, Kobe, Japan
9901
99012 = 98029801.
1 / 9901 = 0.00010099, 102 + 02 + 992 = 9901,
1 / 9901 = 0.00010099, 102 + 0992 = 9901.
99012 = 98029801, and 98 + 0 + 2 + 9801 = 98 + 2 + 9801 = 9802 + 98 + 0 + 1 = 9901.
Page of Squares : First Upload October 27, 2008 ; Last Revised October 27, 2008by Yoshio Mimura, Kobe, Japan
9902
1 / 9902 = 0.00010098969, 102 + 02 + 982 + 92 + 62 + 92 = 9902,
1 / 9902 = 0.00010098969, 102 + 0982 + 92 + 62 + 92 = 9902.
by Yoshio Mimura, Kobe, Japan
9903
The square root of 9903 is 99.5138...., and 99 = 52 + 12 + 32 + 82.
Page of Squares : First Upload October 27, 2008 ; Last Revised October 27, 2008by Yoshio Mimura, Kobe, Japan
9904
99042 = 803 + 2823 + 4223.
Page of Squares : First Upload October 27, 2008 ; Last Revised October 27, 2008by Yoshio Mimura, Kobe, Japan
9905
99052 = 98109025, and 92 + 82 + 12 + 02 + 92 + 02 + 22 + 52 = 162.
Page of Squares : First Upload October 27, 2008 ; Last Revised October 27, 2008by Yoshio Mimura, Kobe, Japan
9906
99062± 5 are primes.
99062 = 393 + 463 + 4613 = 583 + 1953 + 4493.
99062 = 98128836, and 98 * 12 * 8 + 83 * 6 = 9816 + 8 * 46 / 4 = 9818 + 8 + 2 + 81 = 9818 + 82 + 8 + 1 = 9828 - 7 - 3 + 96 = 9914.
99062 = (55 + 56 + 57 + 58 + 59 + 60)2 + (61 + 62 + 63 + 64 + 65 + 66)2 + (67 + 68 + 69 + 70 + 71 + 72)2 + ... + (361 + 362 + 363 + 364 + 365 + 366)2.
Page of Squares : First Upload October 27, 2008 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
9911
99112 = 4332 + 4342 + 4352 + 4362 + 4372 + ... + 7212.
Page of Squares : First Upload October 27, 2008 ; Last Revised October 27, 2008by Yoshio Mimura, Kobe, Japan
9916
99162 = 98327056, a square with different digits.
99162 = 98327056, and 9832 + 70 / 5 * 6 = 9916.
Page of Squares : First Upload October 27, 2008 ; Last Revised October 27, 2008by Yoshio Mimura, Kobe, Japan
9918
99182 = 74 + 634 + 774 + 834.
99182 = 98366724, and 9836 + 6 + 72 + 4 = 9918.
The integral triangle of sides 11267, 17530, 19981 has square area 99182.
Page of Squares : First Upload October 27, 2008 ; Last Revised October 21, 2011by Yoshio Mimura, Kobe, Japan
9919
99192 = 493 + 1303 + 4583 = 1463 + 3613 + 3643 = 2733 + 3183 + 3583.
Page of Squares : First Upload October 27, 2008 ; Last Revised October 27, 2008by Yoshio Mimura, Kobe, Japan
9922
99222 = 114 + 334 + 334 + 994.
99222 = 98446084, and 9844 - 6 + 0 + 84 = 9922.
Page of Squares : First Upload October 27, 2008 ; Last Revised October 27, 2008by Yoshio Mimura, Kobe, Japan
9923
99232 = 98465929, and 9846 + 59 + 2 * 9 = 9923.
Page of Squares : First Upload October 27, 2008 ; Last Revised October 27, 2008by Yoshio Mimura, Kobe, Japan
9924
99242 = 98485776, and 9848 + 5 + 77 - 6 = 9924.
Page of Squares : First Upload October 27, 2008 ; Last Revised October 27, 2008by Yoshio Mimura, Kobe, Japan
9925
99252 = 98505625, and 9850 + 5 * 6 / 2 * 5 = 9925.
Loop of length 35 by the function f(N) = ... + c2 + b2 + a2 where N = ... + 1002c + 100b + a:
9925 - 10426 - 693 - 8685 - ... - 4451 - 4537 - 3394 - 9925
(Note f(9925) = 992 + 252 = 10426, f(10426) = 12 + 042 + 262 = 693, etc. See 37)
by Yoshio Mimura, Kobe, Japan
9926
99262 = 98525476, and 985 / 2 * 5 * 4 + 76 = 9926.
Page of Squares : First Upload October 27, 2008 ; Last Revised October 27, 2008by Yoshio Mimura, Kobe, Japan
9927
99272± 2 are primes.
Page of Squares : First Upload January 11, 2014 ; Last Revised January 11, 2014by Yoshio Mimura, Kobe, Japan
9928
99282 = 184 + 424 + 424 + 984.
1 / 9928 = 0.0001007252215954, 102 + 072 + 22 + 52 + 222 + 152 + 952 + 42 = 9928.
99285 = 96451468093757882368 :
92 + 642 + 512 + 462 + 82 + 02 + 92 + 32 + 72 + 52 + 72 + 82 + 82 + 232 + 62 + 82 = 9928.
by Yoshio Mimura, Kobe, Japan
9931
99314 = 9726843482307121, and
92 + 72 + 22 + 682 + 432 + 482 + 232 + 02 + 72 + 12 + 212 = 9931.
by Yoshio Mimura, Kobe, Japan
9932
99322 = 98644624, and 9 * 8 * 6 / 4 * 46 * 2 - 4 = 9932.
Page of Squares : First Upload October 27, 2008 ; Last Revised October 27, 2008by Yoshio Mimura, Kobe, Japan
9934
99342 = 98684356, and 9868 + 4 * 3 * 5 + 6 = 9934.
Page of Squares : First Upload October 27, 2008 ; Last Revised October 27, 2008by Yoshio Mimura, Kobe, Japan
9936
99362 = 1893 + 3243 + 3873.
Page of Squares : First Upload October 27, 2008 ; Last Revised October 27, 2008by Yoshio Mimura, Kobe, Japan
9937
99372 = 98743969, and 9874 + 3 - 9 + 69 = 9937.
Page of Squares : First Upload October 27, 2008 ; Last Revised October 27, 2008by Yoshio Mimura, Kobe, Japan
9939
99392 = 1693 + 2193 + 4373.
99394 = 9758223534605841, and
92 + 72 + 52 + 822 + 22 + 352 + 32 + 42 + 62 + 02 + 52 + 82 + 412 = 9939.
by Yoshio Mimura, Kobe, Japan
9942
99422 = 98843364, and 9884 + 3 * 3 * 6 + 4 = 9884 - 3 - 3 + 64 = 9942.
Page of Squares : First Upload October 27, 2008 ; Last Revised October 27, 2008by Yoshio Mimura, Kobe, Japan
9944
99442± 3 are primes.
99442 = 743 + 3163 + 4063.
Page of Squares : First Upload October 27, 2008 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
9945
99452 = (122 + 9)(8042 + 9) = (22 + 9)(242 + 9)(1142 + 9).
99452 = 98903025, and 9890 + 30 * 2 - 5 = 9890 + 30 + 25 = 9945.
Komachi equation: 99452 = 12 / 22 * 342 * 52 / 62 * 782 * 92.
Page of Squares : First Upload October 27, 2008 ; Last Revised January 11, 2014by Yoshio Mimura, Kobe, Japan
9946
99462 = 23 + 1933 + 4513.
Page of Squares : First Upload October 27, 2008 ; Last Revised October 27, 2008by Yoshio Mimura, Kobe, Japan
9947
1 / 9947 = 0.00010053282396, 102 + 02 + 52 + 32 + 22 + 82 + 232 + 962 = 9947,
1 / 9947 = 0.00010053282396, 102 + 052 + 32 + 22 + 82 + 232 + 962 = 9947.
by Yoshio Mimura, Kobe, Japan
9953
99532 = 3073 + 3173 + 3373.
Page of Squares : First Upload October 27, 2008 ; Last Revised October 27, 2008by Yoshio Mimura, Kobe, Japan
9954
99542 = 1473 + 1933 + 4463.
Page of Squares : First Upload October 27, 2008 ; Last Revised October 27, 2008by Yoshio Mimura, Kobe, Japan
9955
99552 = 493 + 723 + 4623.
99552 = 99102025, and 92 + 92 + 12 + 02 + 22 + 02 + 22 + 52 = 142.
99552 = 99102025, and 9910 + 20 * 2 + 5 = 9955.
99552 = 99102025, and 9910 + 20 + 25 = 9955.
99554 = 9821211359100625, and
982 + 22 + 12 + 22 + 12 + 132 + 52 + 92 + 12 + 02 + 02 + 62 + 22 + 52 = 9955.
by Yoshio Mimura, Kobe, Japan
9956
99562 = 99121936, and 9912 - 1 + 9 + 36 = 9956.
99565 = 97819275003239883776 :
92 + 72 + 82 + 192 + 272 + 52 + 02 + 02 + 322 + 392 + 82 + 82 + 32 + 772 + 62 = 9956.
by Yoshio Mimura, Kobe, Japan
9957
99572 = 99141849, and 9914 - 1 + 8 + 4 * 9 = 9957.
Page of Squares : First Upload October 27, 2008 ; Last Revised October 27, 2008by Yoshio Mimura, Kobe, Japan
9959
99593 = 987750361079, and 92 + 82 + 772 + 52 + 02 + 32 + 612 + 02 + 72 + 92 = 9959.
Page of Squares : First Upload December 1, 2008 ; Last Revised December 1, 2008by Yoshio Mimura, Kobe, Japan
9963
99632 = 1603 + 2643 + 4253.
99632 = 99261369, and 9 * 9 * 2 / 6 * 1 * 369 = 9963.
99632 = 3243 + 365 + 97.
Page of Squares : First Upload October 27, 2008 ; Last Revised November 29, 2010by Yoshio Mimura, Kobe, Japan
9964
99642 = 99281296, and 9928 + 1 + 29 + 6 = 9964.
Page of Squares : First Upload October 27, 2008 ; Last Revised October 27, 2008by Yoshio Mimura, Kobe, Japan
9966
42+ 172 + ... + (13n +4)2 + ... + 15642 = 99662.
6402k + 9570k + 9966k + 13266k are squares for k = 1,2,3 (1982, 201962, 21126602).
Page of Squares : First Upload October 27, 2008 ; Last Revised July 18, 2011by Yoshio Mimura, Kobe, Japan
9969
99692 = 2363 + 2893 + 3963.
99695 = 98459580255147420849 :
92 + 82 + 452 + 92 + 52 + 802 + 252 + 52 + 12 + 42 + 72 + 42 + 202 + 82 + 42 + 92 = 9969.
by Yoshio Mimura, Kobe, Japan
9972
99722 = 143 + 573 + 4633.
Page of Squares : First Upload October 27, 2008 ; Last Revised October 27, 2008by Yoshio Mimura, Kobe, Japan
9975
99752 = 99500625, and 9950 + 0 * 6 + 25 = 9975.
Page of Squares : First Upload October 27, 2008 ; Last Revised October 27, 2008by Yoshio Mimura, Kobe, Japan
9976
99762 = 1583 + 2583 + 4283.
99762 = 99520576.
Page of Squares : First Upload October 27, 2008 ; Last Revised November 29, 2010by Yoshio Mimura, Kobe, Japan
9977
99772 = 99540529, and 9954 + 0 + 5 + 2 * 9 = 9977.
Page of Squares : First Upload October 27, 2008 ; Last Revised October 27, 2008by Yoshio Mimura, Kobe, Japan
9981
99812 = 1923 + 3453 + 3723.
99812 = 99620361, and 9962 + 0 + 3 * 6 + 1 = 9981.
99815 = 99053603147513573901 :
92 + 92 + 02 + 52 + 32 + 602 + 32 + 12 + 472 + 512 + 352 + 72 + 32 + 92 + 02 + 12 = 9981.
by Yoshio Mimura, Kobe, Japan
9982
99822 = 334 + 634 + 714 + 874.
99825 = 99103234173246910432 :
92 + 92 + 102 + 322 + 32 + 42 + 12 + 732 + 22 + 462 + 92 + 102 + 42 + 322 = 9982.
by Yoshio Mimura, Kobe, Japan
9983
99832 = 99660289, and 9966 + 0 * 2 + 8 + 9 = 9983.
Page of Squares : First Upload October 27, 2008 ; Last Revised October 27, 2008by Yoshio Mimura, Kobe, Japan
9984
99842 = 99680256, and 9968 + 0 + 2 * 5 + 6 = 9984.
Page of Squares : First Upload October 27, 2008 ; Last Revised October 27, 2008by Yoshio Mimura, Kobe, Japan
9986
99862 = 99720196, and 9972 + 0 - 1 + 9 + 6 = 9986.
Page of Squares : First Upload October 27, 2008 ; Last Revised October 27, 2008by Yoshio Mimura, Kobe, Japan
9987
99872 = 553 + 1173 + 4613.
Page of Squares : First Upload October 27, 2008 ; Last Revised October 27, 2008by Yoshio Mimura, Kobe, Japan
9989
99892 = 99780121, and 9978 + 0 + 12 - 1 = 9989.
99895 = 99451208669731888949 :
92 + 92 + 42 + 52 + 12 + 202 + 82 + 62 + 62 + 92 + 72 + 32 + 12 + 82 + 82 + 82 + 942 + 92
= 92 + 942 + 52 + 12 + 202 + 82 + 62 + 62 + 92 + 72 + 32 + 12 + 82 + 82 + 82 + 92 + 42 + 92 = 9989.
by Yoshio Mimura, Kobe, Japan
9990
99902 = (32 + 9)(182 + 9)(1292 + 9) = (32 + 9)(62 + 9)(182 + 9)(192 + 9)
= (32 + 9)(62 + 9)(3512 + 9).
99902 = 1353 + 2373 + 4383.
99902 = 99800100, and 9980 + 0 + 10 + 0 = 9990.
99902 = 99800100, and 9980 - 0 + 10 + 0 = 9990.
Page of Squares : First Upload October 27, 2008 ; Last Revised January 11, 2014by Yoshio Mimura, Kobe, Japan
9991
99912 = 99820081, and 9982 + 0 + 0 + 8 + 1 = 9982 + 0 * 0 + 8 + 1 = 9991.
Page of Squares : First Upload October 27, 2008 ; Last Revised October 27, 2008by Yoshio Mimura, Kobe, Japan
9993
99932 = 164 + 174 + 624 + 964.
Page of Squares : First Upload October 27, 2008 ; Last Revised October 27, 2008by Yoshio Mimura, Kobe, Japan
9994
99942 = 99880036, and 9988 + 0 + 0 * 3 + 6 = 9988 + 0 * 0 * 3 + 6 = 9994.
Page of Squares : First Upload October 27, 2008 ; Last Revised October 27, 2008by Yoshio Mimura, Kobe, Japan
9995
99952 = 99900025, 9990 + 0 + 0 * 2 + 5 = 9990 + 0 * 0 * 2 + 5 = 9995.
Page of Squares : First Upload October 27, 2008 ; Last Revised October 27, 2008by Yoshio Mimura, Kobe, Japan
9996
99962 = 1003 + 2583 + 4343.
Page of Squares : First Upload October 27, 2008 ; Last Revised October 27, 2008by Yoshio Mimura, Kobe, Japan
9997
99972 = 99940009, a square which consistes of 3 kinds of digits 0,4,9.
A = 9997
1 / A = 0.0001000300090027008102, 102 + 02 + 0302 + 00902 + 0272 + 0082 + 102 + 22 = A,
1 / A = 0.0001000300090027008102, 102 + 002 + 302 + 00902 + 0272 + 0082 + 102 + 22 = A,
1 / A = 0.0001000300090027008102, 102 + 00302 + 02 + 0902 + 0272 + 0082 + 102 + 22 = A,
1 / A = 0.0001000300090027008102, 102 + 00302 + 002 + 902 + 0272 + 0082 + 102 + 22 = A,
1 / A = 0.0001000300090027008102, 102 + 00302 + 00902 + 02 + 272 + 0082 + 102 + 22 = A,
1 / A = 0.0001000300090027008102, 102 + 00302 + 00902 + 0272 + 02 + 082 + 102 + 22 = A,
1 / A = 0.0001000300090027008102, 102 + 00302 + 00902 + 0272 + 002 + 82 + 102 + 22 = A,
1 / A = 0.0001000300090027008102, 102 + 00302 + 00902 + 0272 + 0082 + 102 + 22 = A.
by Yoshio Mimura, Kobe, Japan
9999
A cubic polynomial:
(X + 1922)(X + 28282)(X + 99992) = X3 + 103932X2 + 283474682X + 54292170242.
99992 = 99980001, and 9998 + 0 + 0 + 0 + 1 = 9998 + 0 + 0 * 0 + 1 = 9998 + 0 * 0 + 0 + 1
= 9998 + 0 * 0 * 0 + 1 = 9999.
by Yoshio Mimura, Kobe, Japan