7904
79042 = 62473216, and
6 + 247 * 32 - 1 * 6 = 6 + 247 * 32 * 1 - 6 = 6 * 247 * 32 * 1 / 6 = 7904.
by Yoshio Mimura, Kobe, Japan
7908
79082 = 62536464, a zigzag square.
Page of Squares : First Upload June 9, 2008 ; Last Revised June 9, 2008by Yoshio Mimura, Kobe, Japan
7911
79112 = 543 + 1203 + 3933.
Page of Squares : First Upload June 9, 2008 ; Last Revised June 9, 2008by Yoshio Mimura, Kobe, Japan
7912
79122 = 344 + 384 + 464 + 864.
Page of Squares : First Upload June 9, 2008 ; Last Revised June 9, 2008by Yoshio Mimura, Kobe, Japan
7914
79142 = 62631396, and 6 + 2631 * 3 + 9 + 6 = 7914.
Page of Squares : First Upload June 9, 2008 ; Last Revised June 9, 2008by Yoshio Mimura, Kobe, Japan
7915
79155 = 31063801043587946875 :
32 + 102 + 62 + 32 + 82 + 02 + 102 + 432 + 582 + 72 + 92 + 462 + 82 + 72 + 52 = 7915.
by Yoshio Mimura, Kobe, Japan
7916
79162 = 1763 + 1913 + 3693.
79165 = 31083429376743320576 :
32 + 12 + 02 + 82 + 342 + 22 + 92 + 372 + 62 + 72 + 432 + 32 + 22 + 02 + 572 + 62 = 7916.
by Yoshio Mimura, Kobe, Japan
7917
79172 = 1223 + 1563 + 3853.
Page of Squares : First Upload June 9, 2008 ; Last Revised June 9, 2008by Yoshio Mimura, Kobe, Japan
7918
79183 = 496416824632, and 42 + 92 + 62 + 42 + 12 + 682 + 22 + 462 + 322 = 7918.
Page of Squares : First Upload December 1, 2008 ; Last Revised December 1, 2008by Yoshio Mimura, Kobe, Japan
7920
79202 = (22 - 1)(192 - 1)(2412 - 1) = (22 - 1)(232 - 1)(1992 - 1) = (22 - 1)(42 - 1)(52 - 1)(2412 - 1)
= (42 - 1)(232 - 1)(892 - 1) = (42 - 1)(92 - 1)(102 - 1)(232 - 1) = (92 - 1)(102 - 1)(892 - 1).
by Yoshio Mimura, Kobe, Japan
7921
The square of 89.
Page of Squares : First Upload June 9, 2008 ; Last Revised June 9, 2008by Yoshio Mimura, Kobe, Japan
7922
79222 = 62758084, a zigzag square.
Page of Squares : First Upload June 9, 2008 ; Last Revised June 9, 2008by Yoshio Mimura, Kobe, Japan
7923
79234 = 3940566162097041,
and 32 + 92 + 402 + 52 + 662 + 12 + 62 + 22 + 02 + 92 + 72 + 02 + 412 = 7923.
79235 = 31221105702294855843 :
312 + 222 + 112 + 02 + 52 + 72 + 02 + 222 + 92 + 482 + 52 + 582 + 42 + 32
= 32 + 12 + 222 + 112 + 02 + 572 + 02 + 222 + 92 + 42 + 82 + 52 + 582 + 42 + 32 = 7923.
by Yoshio Mimura, Kobe, Japan
7926
1 / 7926 = 0.00012616704...., and 12616704 = 35522.
Page of Squares : First Upload June 9, 2008 ; Last Revised June 9, 2008by Yoshio Mimura, Kobe, Japan
7927
79272 = 62837329, and 62 + 22 + 82 + 32 + 72 + 32 + 22 + 92 = 162.
79272 = 144 + 414 + 744 + 744.
Page of Squares : First Upload June 9, 2008 ; Last Revised June 9, 2008by Yoshio Mimura, Kobe, Japan
7929
79292 = 62869041, a zigzag square.
79292 = 663 + 2083 + 3773 = 484 + 604 + 604 + 754.
Page of Squares : First Upload June 9, 2008 ; Last Revised June 9, 2008by Yoshio Mimura, Kobe, Japan
7930
79302± 3 are primes.
79302 = (12 + 9)(282 + 9)(892 + 9).
79302 = S2(232) + S2(560), where S2(n) = 12 + 22 + 32 + 42 + ... + n2.
Page of Squares : First Upload June 9, 2008 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
7932
79322 = 393 + 2573 + 3583.
79325 = 31398834497321106432 :
32 + 132 + 92 + 82 + 82 + 32 + 442 + 92 + 732 + 22 + 112 + 02 + 62 + 42 + 32 + 22 = 7932.
by Yoshio Mimura, Kobe, Japan
7938
79382 = (12 + 5)(22 + 5)(42 + 5)(72 + 5)(322 + 5) = (12 + 5)(322 + 5)(1012 + 5)
= (22 + 5)(72 + 5)(112 + 5)(322 + 5) = (42 + 5)(172 + 5)(1012 + 5).
79382 = 1293 + 2143 + 3713 = 634 + 634 + 634 + 634.
79385 = 31517769340217307168 :
32 + 12 + 52 + 12 + 72 + 72 + 62 + 92 + 342 + 02 + 212 + 72 + 302 + 712 + 62 + 82
= 32 + 152 + 172 + 72 + 62 + 92 + 32 + 402 + 212 + 72 + 32 + 02 + 712 + 62 + 82 = 7938.
Komachi equations: 79382 = 982 / 72 / 62 * 542 * 32 * 212.
Page of Squares : First Upload June 9, 2008 ; Last Revised January 11, 2014br /> by Yoshio Mimura, Kobe, Japan7939
The square root of 7939 is 89.1010662113...., and
89 = 12 + 02 + 12 + 02 + 62 + 62 + 22 + 12 + 12 + 32.
by Yoshio Mimura, Kobe, Japan
7941
79412 = 63059481, a square with different digits.
Page of Squares : First Upload June 9, 2008 ; Last Revised June 9, 2008by Yoshio Mimura, Kobe, Japan
7943
79432 = (121 + 122)2 + (123 + 124)2 + (125 + 126)2 + ... + (457 + 458)2.
Page of Squares : First Upload June 9, 2008 ; Last Revised June 9, 2008by Yoshio Mimura, Kobe, Japan
7944
79442 = 203 + 1003 + 3963 = 2423 + 2563 + 3183.
Page of Squares : First Upload June 9, 2008 ; Last Revised June 9, 2008by Yoshio Mimura, Kobe, Japan
7945
79452 = 10992 + 11002 + 11012 + 11022 + ... + 11482.
Page of Squares : First Upload June 9, 2008 ; Last Revised June 9, 2008by Yoshio Mimura, Kobe, Japan
7946
79462 = 1803 + 2673 + 3373.
Page of Squares : First Upload June 9, 2008 ; Last Revised June 9, 2008by Yoshio Mimura, Kobe, Japan
7947
79472 = 63154809, a square with different digits.
Loop of length 56 by the function f(N) = ... + c2 + b2 + a2 where N = ... + 1002c + 100b + a:
7947 - 8450 - 9556 - 12161 - ... - 9140 - 9881 - 16165 - 7947
(Note f(7947) = 792 + 472 = 8450, f(8450) = 842 + 502 = 9556, etc. See 41)
79475 = 31696847113921044507 :
32 + 162 + 92 + 62 + 82 + 42 + 712 + 132 + 92 + 22 + 102 + 42 + 452 + 02 + 72 = 7947.
by Yoshio Mimura, Kobe, Japan
7950
79502 = (102 + 6)(122 + 6)(632 + 6) = (22 + 6)(32 + 6)(102 + 6)(632 + 6).
Page of Squares : First Upload January 11, 2014 ; Last Revised January 11, 2014by Yoshio Mimura, Kobe, Japan
7953
79534 = 4000588938543681,
and 402 + 02 + 02 + 52 + 82 + 82 + 92 + 382 + 52 + 42 + 32 + 682 + 12 = 7953.
by Yoshio Mimura, Kobe, Japan
7955
79552 = 1963 + 2253 + 3543.
7955 = (12 + 22 + 32 + ... + 1292) / (12 + 22 + 32 + ... + 62).
Page of Squares : First Upload June 9, 2008 ; Last Revised November 25, 2008by Yoshio Mimura, Kobe, Japan
7956
79562 = 63297936, and 6 + 3 + 2 + 9 + 7936 = 6 / 3 + 2 * 9 + 7936
= 63 * 2 * 9 * 7 + 9 + 3 + 6 = 63 * 2 * 9 * 7 + 9 / 3 * 6 = 632 * 9 + 7 * 9 * 36 = 7956.
by Yoshio Mimura, Kobe, Japan
7957
7957 = (12 + 22 + 32 + ... + 1092) / (12 + 22 + 32 + 42 + 52).
79572 = 63313849, and 62 + 32 + 32 + 12 + 32 + 82 + 42 + 92 = 152.
Page of Squares : First Upload June 9, 2008 ; Last Revised November 25, 2008by Yoshio Mimura, Kobe, Japan
7958
The square root of 7958 is 89.2076...., and 89 = 22 + 02 + 72 + 62.
Page of Squares : First Upload June 9, 2008 ; Last Revised June 9, 2008by Yoshio Mimura, Kobe, Japan
7959
7959 = (12 + 22 + 32 + ... + 1892) / (12 + 22 + 32 + ... + 92).
79592 = 63345681, and 62 + 32 + 32 + 42 + 52 + 62 + 82 + 12 = 142.
The quadratic polynomial -7959X2 + 67284X - 43196 takes the values 1272, 2442, 2952, 3142, 3072, 2722 at X = 1, 2,..., 6,
Page of Squares : First Upload June 9, 2008 ; Last Revised December 15, 2008by Yoshio Mimura, Kobe, Japan
7961
7961 = (12 + 22 + 32 + ... + 2092) / (12 + 22 + 32 + ... + 102).
Page of Squares : First Upload November 25, 2008 ; Last Revised November 25, 2008by Yoshio Mimura, Kobe, Japan
7962
79622 = 2003 + 2893 + 3153.
Page of Squares : First Upload June 9, 2008 ; Last Revised June 9, 2008by Yoshio Mimura, Kobe, Japan
7964
79642 = 63425296, a zigzag square.
Page of Squares : First Upload June 9, 2008 ; Last Revised June 9, 2008by Yoshio Mimura, Kobe, Japan
7965
79652 = 63441225, and 6 * 3 * 441 + 2 + 25 = 6 * 3 * 441 + 22 + 5 = 7965.
3245k + 7965k + 101185k + 235705k are squares for k = 1,2,3 (5902, 2566502, 1188761502).
Page of Squares : First Upload June 9, 2008 ; Last Revised July 12, 2011by Yoshio Mimura, Kobe, Japan
7966
79662 = 63457156, and 6 * 3 * 45 + 7156 = 7966.
Page of Squares : First Upload June 9, 2008 ; Last Revised June 9, 2008by Yoshio Mimura, Kobe, Japan
7969
79692 = 63504961, and 63504 = 2522 and 961 = 312.
79692 = 653 + 3083 + 3243.
Page of Squares : First Upload June 9, 2008 ; Last Revised June 9, 2008by Yoshio Mimura, Kobe, Japan
7971
79712 = 63536841, and 62 + 32 + 52 + 32 + 62 + 82 + 42 + 12 = 142.
Page of Squares : First Upload June 9, 2008 ; Last Revised June 9, 2008by Yoshio Mimura, Kobe, Japan
7973
79732 = 1343 + 1603 + 3853.
4165k + 7973k + 17017k + 27489k are squares for k = 1,2,3 (2382, 335582, 51262822).
Page of Squares : First Upload June 9, 2008 ; Last Revised July 12, 2011by Yoshio Mimura, Kobe, Japan
7976
79762 = 63616576, a zigzag square.
The square root of 7976 is 89.3084...., and 89 = 32 + 02 + 82 + 42.
Loop of length 56 by the function f(N) = ... + c2 + b2 + a2 where N = ... + 1002c + 100b + a:
7976 - 12017 - 690 - 8136 - ... - 3617 - 1585 - 7450 - 7976
(Note f(7976) = 792 + 762 = 12017, f(12017) = 12 + 202 + 172 = 690, etc. See 41)
by Yoshio Mimura, Kobe, Japan
7977
79775 = 32299660704307203657 :
322 + 292 + 92 + 62 + 62 + 02 + 72 + 02 + 42 + 302 + 72 + 202 + 362 + 572 = 7977.
by Yoshio Mimura, Kobe, Japan
7978
79782 = 63648484, a zigzag square.
Page of Squares : First Upload June 9, 2008 ; Last Revised June 9, 2008by Yoshio Mimura, Kobe, Japan
7979
79792 = 63664441, and 6 + 3 * 664 * 4 + 4 + 1 = 7979.
Page of Squares : First Upload June 9, 2008 ; Last Revised June 9, 2008by Yoshio Mimura, Kobe, Japan
7980
79802 = (22 - 1)(62 - 1)(202 - 1)(392 - 1).
The integral triangle of sides 3249, 159250, 162401 has square area 79802.
Page of Squares : First Upload October 18, 2011 ; Last Revised January 11, 2014by Yoshio Mimura, Kobe, Japan
7981
79812 = 63696361, a square pegged by 6.
Page of Squares : First Upload June 9, 2008 ; Last Revised June 9, 2008by Yoshio Mimura, Kobe, Japan
7982
1 / 7982 = 0.00012528188, 122 + 52 + 22 + 82 + 12 + 882 = 7982.
130k + 1794k + 6994k + 7982k are squares for k = 1,2,3 (1302, 107642, 9254442).
79825 = 32401015151717150432 :
32 + 22 + 402 + 12 + 02 + 12 + 512 + 512 + 72 + 12 + 72 + 12 + 52 + 02 + 42 + 322
= 322 + 402 + 12 + 02 + 12 + 512 + 512 + 72 + 12 + 72 + 12 + 52 + 02 + 42 + 32 + 22 = 7982.
by Yoshio Mimura, Kobe, Japan
7983
79832 = 84 + 94 + 444 + 884 = 424 + 664 + 664 + 694.
Page of Squares : First Upload June 9, 2008 ; Last Revised June 9, 2008by Yoshio Mimura, Kobe, Japan
7984
79842 = 393 + 2943 + 3373.
Page of Squares : First Upload June 9, 2008 ; Last Revised June 9, 2008by Yoshio Mimura, Kobe, Japan
7985
79852 = (12 + 4)(35712 + 4).
Page of Squares : First Upload January 11, 2014 ; Last Revised January 11, 2014by Yoshio Mimura, Kobe, Japan
7986
79862 = 1213 + 2423 + 3633.
Page of Squares : First Upload June 9, 2008 ; Last Revised June 9, 2008by Yoshio Mimura, Kobe, Japan
7987
79872 = 63792169, and 63 + 7921 - 6 + 9 = 7987.
Page of Squares : First Upload June 9, 2008 ; Last Revised June 9, 2008by Yoshio Mimura, Kobe, Japan
7989
79892 = 63824121, a zigzag square.
79894 = 4073518421422641,
and 42 + 02 + 72 + 32 + 512 + 82 + 422 + 12 + 422 + 22 + 62 + 412 = 7989.
by Yoshio Mimura, Kobe, Japan
7990
79902 = 2102 + 2112 + 2122 + 2132 + ... + 5852.
Page of Squares : First Upload June 9, 2008 ; Last Revised June 9, 2008by Yoshio Mimura, Kobe, Japan
7991
79912 = 63856081, a zigzag square.
79914 = 4077599080678561,
and 402 + 772 + 52 + 92 + 92 + 02 + 82 + 02 + 62 + 72 + 82 + 52 + 62 + 12 = 7991.
by Yoshio Mimura, Kobe, Japan
7994
79942± 3 are primes.
79945 = 32645304181811832224 :
32 + 22 + 62 + 42 + 52 + 302 + 42 + 12 + 82 + 12 + 812 + 182 + 32 + 22 + 22 + 22 + 42
= 32 + 22 + 62 + 42 + 52 + 302 + 42 + 12 + 812 + 82 + 12 + 182 + 32 + 22 + 22 + 22 + 42
= 32 + 22 + 62 + 42 + 52 + 302 + 42 + 182 + 12 + 812 + 12 + 82 + 32 + 22 + 22 + 22 + 42 = 7994.
by Yoshio Mimura, Kobe, Japan
7995
Komachi equations:
79952 = 1232 / 42 * 52 * 62 * 782 / 92 = 1232 * 452 / 62 * 782 / 92.
by Yoshio Mimura, Kobe, Japan
7996
79964 = 4087814141952256,
and 42 + 02 + 82 + 72 + 82 + 142 + 12 + 412 + 92 + 522 + 22 + 562 = 7996.
by Yoshio Mimura, Kobe, Japan
7998
79982 = 63968004, and 6 + 3 - 9 - 6 + 8004 = 7998.
Page of Squares : First Upload June 9, 2008 ; Last Revised June 9, 2008by Yoshio Mimura, Kobe, Japan
7999
79995 = 32747525119360039999 :
32 + 272 + 42 + 72 + 522 + 512 + 12 + 92 + 32 + 62 + 02 + 02 + 392 + 92 + 92 + 92 = 7999.
by Yoshio Mimura, Kobe, Japan