7700
77002 = (22 + 6)(42 + 6)(82 + 6)(622 + 6).
Page of Squares : First Upload January 11, 2014 ; Last Revised January 11, 2014by Yoshio Mimura, Kobe, Japan
7701
77012 = 43 + 2333 + 3603.
Page of Squares : First Upload May 26, 2008 ; Last Revised May 26, 2008by Yoshio Mimura, Kobe, Japan
7703
77032 = 253 + 2963 + 3223.
Page of Squares : First Upload May 26, 2008 ; Last Revised May 26, 2008by Yoshio Mimura, Kobe, Japan
7704
77042 = 59351616, a zigzag square.
Page of Squares : First Upload May 26, 2008 ; Last Revised May 26, 2008by Yoshio Mimura, Kobe, Japan
7705
77052 = 1383 + 1533 + 3763.
Page of Squares : First Upload May 26, 2008 ; Last Revised May 26, 2008by Yoshio Mimura, Kobe, Japan
7706
77062 = 59382436, a zigzag square.
7706 = 592 + 652 and 5965 = 772 + 062.
Page of Squares : First Upload May 26, 2008 ; Last Revised October 9, 2008by Yoshio Mimura, Kobe, Japan
7707
77072 = 59397849, a zigzag square.
Page of Squares : First Upload May 26, 2008 ; Last Revised May 26, 2008by Yoshio Mimura, Kobe, Japan
7708
77082 = 93 + 2363 + 3593 = 464 + 644 + 644 + 684.
Page of Squares : First Upload May 26, 2008 ; Last Revised May 26, 2008by Yoshio Mimura, Kobe, Japan
7709
1 / 7709 = 0.0001297185108314, 122 + 92 + 72 + 182 + 52 + 12 + 0832 + 142 = 7709.
Page of Squares : First Upload May 26, 2008 ; Last Revised May 26, 2008by Yoshio Mimura, Kobe, Japan
7711
1 / N = 0.0001296...., and 1296 = 362 for N = 7711, 7712, 7713, 7714, 7715 and 7716.
Page of Squares : First Upload May 26, 2008 ; Last Revised May 26, 2008by Yoshio Mimura, Kobe, Japan
7712
1 / 7712 = 0.0001296680497, 12 + 292 + 662 + 82 + 02 + 492 + 72 = 7712,
1 / 7712 = 0.0001296680497, 12 + 292 + 662 + 82 + 0492 + 72 = 7712.
77122 = 1243 + 1643 + 3763.
Page of Squares : First Upload May 26, 2008 ; Last Revised May 26, 2008by Yoshio Mimura, Kobe, Japan
7713
77132 = 303 + 2643 + 3453.
Page of Squares : First Upload May 26, 2008 ; Last Revised May 26, 2008by Yoshio Mimura, Kobe, Japan
7715
77152 = 59521225,
and 52 + 92 + 52 + 22 + 12 + 22 + 22 + 52 = 132.
77155 = 27332518579737321875 : 22 + 72 + 32 + 32 + 22 + 52 + 12 + 852 + 72 + 92 + 72 + 32 + 72 + 32 + 22 + 12 + 82 + 72 + 52 = 7715.
Page of Squares : First Upload May 26, 2008 ; Last Revised December 8, 2008by Yoshio Mimura, Kobe, Japan
7716
77162 = 1503 + 2863 + 3203.
Page of Squares : First Upload May 26, 2008 ; Last Revised May 26, 2008by Yoshio Mimura, Kobe, Japan
7721
77212 = 423 + 2983 + 3213.
Page of Squares : First Upload May 26, 2008 ; Last Revised May 26, 2008by Yoshio Mimura, Kobe, Japan
7722
1378k + 3354k + 4446k + 7722k are squares for k = 1,2,3 (1302 ,96202, 7672602).
Page of Squares : First Upload July 12, 2011 ; Last Revised July 12, 2011by Yoshio Mimura, Kobe, Japan
7723
77234 = 3557493697483441,
and 32 + 52 + 572 + 42 + 92 + 362 + 92 + 72 + 42 + 82 + 342 + 412 = 7723.
by Yoshio Mimura, Kobe, Japan
7725
77252 = 59675625, a zigzag square.
77255 = 27510117192861328125 :
22 + 752 + 12 + 02 + 12 + 12 + 72 + 192 + 22 + 82 + 62 + 132 + 282 + 12 + 252
= 22 + 752 + 12 + 02 + 12 + 12 + 72 + 192 + 282 + 62 + 132 + 22 + 82 + 12 + 252 = 7725.
by Yoshio Mimura, Kobe, Japan
7727
77272 = 1703 + 2333 + 3483.
Page of Squares : First Upload May 26, 2008 ; Last Revised May 26, 2008by Yoshio Mimura, Kobe, Japan
7729
77292 = 59737441, and 5 * 9 * 7 / 3 * 74 - 41 = 7729.
77295 = 27581414594518929649 :
22 + 72 + 52 + 82 + 142 + 12 + 452 + 92 + 42 + 512 + 82 + 92 + 22 + 92 + 62 + 492 = 7729.
by Yoshio Mimura, Kobe, Japan
7730
Loop of length 6 by the function f(N) = b2 + a2 for N = 100b + a:
7730 - 6829 - 5465 - 7141 - 6722 - 4973 - 7730 (Note f(7730) = 772 + 302 = 6829)
by Yoshio Mimura, Kobe, Japan
7732
77322 = 59783824,a zigzag square.
77325 = 27634984592470930432 :
22 + 72 + 62 + 32 + 492 + 82 + 42 + 52 + 92 + 22 + 472 + 02 + 92 + 302 + 432 + 22 = 7732.
by Yoshio Mimura, Kobe, Japan
7733
77332 = (3 + 4 + 5 + ... + 21)2 + (22 + 23 + 24 + ... + 40)2 + (41 + 42 + 43 + ... + 59)2 + ... + (193 + 194 + 195 + ... + 211)2.
Page of Squares : First Upload May 26, 2008 ; Last Revised May 26, 2008by Yoshio Mimura, Kobe, Japan
7736
77362 = 59845696 appears in the decimal expressions of e:
e = 2.71828•••59845696••• (from the 32188th digit)
(59845696 is the seventh 8-digit square in the expression of e.)
by Yoshio Mimura, Kobe, Japan
7740
Komachi equation: 77402 = 92 * 82 / 72 / 62 * 52 * 432 * 212.
Page of Squares : First Upload November 9, 2010 ; Last Revised November 9, 2010by Yoshio Mimura, Kobe, Japan
7742
77422 = (137 + 138 + 139 + 140 + 141 + 142 + 143)2 + (144 + 145 + 146 + 147 + 148 + 149 + 150)2 + (298 + 299 + 300 + 301 + 302 + 303 + 304)2.
Page of Squares : First Upload May 26, 2008 ; Last Revised May 26, 2008by Yoshio Mimura, Kobe, Japan
7744
The square of 88.
77442 = (22 + 7)(312 + 7)(752 + 7) = (22 + 7)(52 + 7)(132 + 7)(312 + 7).
77442 = 1923 + 2723 + 3203.
Page of Squares : First Upload May 26, 2008 ; Last Revised January 11, 2014by Yoshio Mimura, Kobe, Japan
7747
77475 = 27904084592223763507 :
272 + 92 + 02 + 402 + 82 + 452 + 92 + 22 + 222 + 372 + 62 + 352 + 02 + 72
= 272 + 92 + 02 + 402 + 82 + 452 + 92 + 222 + 22 + 372 + 62 + 352 + 02 + 72 = 7747.
by Yoshio Mimura, Kobe, Japan
7748
77482 = 1023 + 2913 + 3253.
77482 = 5102 + 5112 + 5122 + 5132 + ... + 6782.
Page of Squares : First Upload May 26, 2008 ; Last Revised May 26, 2008by Yoshio Mimura, Kobe, Japan
7749
77492 = (22 + 5)(42 + 5)(62 + 5)(882 + 5).
77492 = 1263 + 2253 + 3603 = 2353 + 2513 + 3153.
Page of Squares : First Upload May 26, 2008 ; Last Revised January 11, 2014by Yoshio Mimura, Kobe, Japan
7750
77502 + 77512 + 77522 + ... + 78122 = 78132 + 78142 + 78152 + ... + 78742.
Page of Squares : First Upload September 16, 2011 ; Last Revised September 16, 2011by Yoshio Mimura, Kobe, Japan
7752
77522 = (122 + 8)(202 + 8)(312 + 8) = (32 + 8)(42 + 8)(122 + 8)(312 + 8)
= (32 + 8)(72 + 8)(122 + 8)(202 + 8).
77522 = 24 + 184 + 624 + 824.
Page of Squares : First Upload May 26, 2008 ; Last Revised January 11, 2014by Yoshio Mimura, Kobe, Japan
7755
77552± 2 are primes.
77552 = 13 + 1743 + 3803.
Page of Squares : First Upload May 26, 2008 ; Last Revised January 11, 2014by Yoshio Mimura, Kobe, Japan
7758
77585 = 28102753647366252768 :
282 + 12 + 02 + 22 + 72 + 52 + 362 + 42 + 732 + 62 + 62 + 22 + 52 + 22 + 72 + 62 + 82 = 7758.
by Yoshio Mimura, Kobe, Japan
7759
77592 = 60202081, a zigzag square.
Page of Squares : First Upload May 26, 2008 ; Last Revised May 26, 2008by Yoshio Mimura, Kobe, Japan
7761
77612± 2 are primes.
77612 = 60233121, and 62 + 02 + 22 + 32 + 32 + 12 + 22 + 12 = 82.
77615 = 28157132024374374801 :
22 + 82 + 12 + 52 + 712 + 32 + 22 + 02 + 242 + 32 + 72 + 432 + 72 + 42 + 82 + 02 + 12 = 7761.
by Yoshio Mimura, Kobe, Japan
7762
77622 = 60248644, a square with even digits.
77622± 3 are primes.
1 / 7762 = 0.000128832, 12 + 22 + 882 + 32 + 22 = 7762.
Page of Squares : First Upload May 26, 2008 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
7766
77662 = 1793 + 1963 + 3613.
Page of Squares : First Upload May 26, 2008 ; Last Revised May 26, 2008by Yoshio Mimura, Kobe, Japan
7767
77672 = 60326289, and 603 * 26 / 2 - 8 * 9 = 7767.
Page of Squares : First Upload May 26, 2008 ; Last Revised May 26, 2008by Yoshio Mimura, Kobe, Japan
7768
77684 = 3641135723646976,
and 32 + 62 + 412 + 12 + 32 + 52 + 72 + 22 + 32 + 62 + 42 + 62 + 92 + 762 = 7768.
by Yoshio Mimura, Kobe, Japan
7771
1 / 7771 = 0.00012868356, 12 + 282 + 62 + 832 + 52 + 62 = 7771.
The square root of 7771 is 88.15327...., and 88 = 12 + 52 + 32 + 22 + 72.
77712 = S2(160) + S2(561), where S2(n) = 12 + 22 + 32 + ... + n2.
Page of Squares : First Upload May 26, 2008 ; Last Revised May 26, 2008by Yoshio Mimura, Kobe, Japan
7772
77722 = 24 + 484 + 484 + 844.
Page of Squares : First Upload May 26, 2008 ; Last Revised May 26, 2008by Yoshio Mimura, Kobe, Japan
7774
77742 = 60435076 is a zigzag square.
77742 = S2(430) + S2(466), where S2(n) = 12 + 22 + 32 + ... + n2.
Page of Squares : First Upload May 26, 2008 ; Last Revised May 26, 2008by Yoshio Mimura, Kobe, Japan
7775
The sum of (24x - 1)2 taken over x = 1,2,...,7775 is 809822.
Page of Squares : First Upload May 26, 2008 ; Last Revised May 26, 2008by Yoshio Mimura, Kobe, Japan
7776
77762 = (22 + 8)(42 + 8)(102 + 8)(442 + 8).
902 + 7776 = 1262, 902 - 7776 = 182.
77762 = 363 + 1563 + 3843 = 1353 + 1983 + 3693 = 1803 + 2253 + 3513.
Page of Squares : First Upload May 26, 2008 ; Last Revised January 11, 2014by Yoshio Mimura, Kobe, Japan
7777
77772 = 60481729, a square with different digits.
77772 = 60481729, and 6048 + 1729 = 7777.
77772 = 64 + 514 + 544 + 824 = 15 + 65 + 65 + 365.
77774 = 3658039542829441,
and 32 + 62 + 582 + 02 + 392 + 52 + 42 + 282 + 22 + 92 + 442 + 12 = 7777.
by Yoshio Mimura, Kobe, Japan
7778
77782 = 60497284, and 6 + 0 * 4 + 972 * 8 - 4 = 7778.
Page of Squares : First Upload May 26, 2008 ; Last Revised May 26, 2008by Yoshio Mimura, Kobe, Japan
7782
1 / 7782 = 0.000128501670521, 12 + 22 + 852 + 012 + 62 + 72 + 052 + 212 = 7782.
77822 = 1033 + 2693 + 3423.
Page of Squares : First Upload May 26, 2008 ; Last Revised May 26, 2008by Yoshio Mimura, Kobe, Japan
7784
77842± 3 are primes.
77842 = 583 + 2303 + 3643.
Page of Squares : First Upload May 26, 2008 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
7785
Loop of length 56 by the function f(N) = ... + c2 + b2 + a2 where N = ... + 1002c + 100b + a:
7785 - 13154 - 3878 - 7528 - ... - 3796 - 10585 - 7251 - 7785
(Note f(7785) = 772 + 852 = 13154, f(13154) = 12 + 312 + 542 = 3878, etc. See 41)
by Yoshio Mimura, Kobe, Japan
7787
77872 = 60637369, and 62 + 02 + 62 + 32 + 72 + 32 + 62 + 92 = 162.
77872 = 4232 + 4252 + 4272 + 4292 + ... + 7592.
Page of Squares : First Upload May 26, 2008 ; Last Revised May 26, 2008by Yoshio Mimura, Kobe, Japan
7788
77882 = 1063 + 1763 + 3783.
Page of Squares : First Upload May 26, 2008 ; Last Revised May 26, 2008by Yoshio Mimura, Kobe, Japan
7789
77892 = 203 + 1923 + 3773.
Page of Squares : First Upload May 26, 2008 ; Last Revised May 26, 2008by Yoshio Mimura, Kobe, Japan
7791
77912 = 60699681, and 6 + 0 * 6 + 9 + 96 * 81 = 6 * 0 + 6 + 9 + 96 * 81 = 7791.
77912 = 773 + 1473 + 3853.
77914 = 3684451273501761,
and 32 + 62 + 82 + 42 + 42 + 512 + 22 + 72 + 352 + 02 + 12 + 72 + 612 = 7791.
by Yoshio Mimura, Kobe, Japan
7792
77922 = 60715264, a zigzag square.
1 / 7792 = 0.00012833675564, 12 + 282 + 32 + 362 + 752 + 52 + 62 + 42 = 7792,
1 / 7792 = 0.00012833675564, 122 + 82 + 32 + 32 + 672 + 552 + 62 + 42 = 7792.
77922 = 164 + 164 + 284 + 884.
Page of Squares : First Upload May 26, 2008 ; Last Revised May 26, 2008by Yoshio Mimura, Kobe, Japan
7794
77944 = 3690129486702096,
and 32 + 62 + 92 + 02 + 12 + 22 + 92 + 42 + 862 + 72 + 02 + 22 + 02 + 92 + 62 = 7794.
77945 = 28760869219356136224 :
22 + 82 + 72 + 602 + 82 + 62 + 92 + 212 + 92 + 32 + 562 + 132 + 62 + 22 + 22 + 42 = 7794.
by Yoshio Mimura, Kobe, Japan
7796
77962 = 60777616, and 62 + 02 + 72 + 72 + 72 + 62 + 12 + 62 = 162.
Page of Squares : First Upload May 26, 2008 ; Last Revised May 26, 2008by Yoshio Mimura, Kobe, Japan
7797
77975 = 28816263789256358757 :
22 + 82 + 82 + 12 + 62 + 22 + 62 + 32 + 72 + 82 + 92 + 22 + 52 + 632 + 52 + 82 + 72 + 572
= 22 + 82 + 82 + 12 + 62 + 22 + 632 + 72 + 82 + 92 + 22 + 52 + 62 + 32 + 52 + 82 + 72 + 572 = 7797.
by Yoshio Mimura, Kobe, Japan
7798
77982 = 60808804, a square with even digits.
77982 = 93 + 833 + 3923.
Page of Squares : First Upload May 26, 2008 ; Last Revised May 26, 2008by Yoshio Mimura, Kobe, Japan
7799
77992 = 1763 + 3003 + 3053.
Page of Squares : First Upload May 26, 2008 ; Last Revised May 26, 2008by Yoshio Mimura, Kobe, Japan