The smallest squares containing k 46's :
4624 = 682, 21464689 = 46332, 924646464 = 304082,
4464646446841 = 21129712, 2646546046046464 = 514445922.
46 is the sum of m squares for m = 3, 4, ..., 32.
The third integer which is the sum of 4 distinct squares: 12 + 22 + 42 + 52.
The first integer which is the sum of 8 squares in just 5 ways (see 45).
462 is the first square which is the sum of 8 fourth powers : [1, 2, 3, 4, 4, 4, 5, 5].
46k + 170k + 202k + 258k are squares for k = 1,2,3 (262, 3722, 55162).
190k + 338k + 786k + 802k are squares for k = 1,2,3 (462, 11882, 323562).
Komachi Fraction : 462 = 1275948/603.
Komachi equations:
462 = 1 - 2 + 345 * 6 + 7 * 8 - 9 = 1 - 234 + 5 * 6 * 78 + 9
= 12 * 34 * 5 - 6 - 7 + 89,
462 = 9 * 8 * 7 * 6 - 5 - 43 * 21 = - 9 + 8 - 7 * 6 + 5 * 432 - 1,
462 = 9 - 8 * 76 + 543 / 2 * 10,
462 = 122 * 32 + 42 + 52 * 62 + 72 - 82 - 92,
462 = 92 + 82 * 72 - 62 - 52 - 42 - 322 * 12 = 92 + 82 * 72 - 62 - 52 - 42 - 322 / 12.
(462 + 4) = (62 + 4)(72 + 4) = (12 + 4)(22 + 4)(72 + 4),
(462 + 8) = (22 + 8)(132 + 8).
(1 + 2)(3 + 4 + ... + 30)(31 + 32 + ... + 46) = 9242,
(1 + 2 + ... + 16)(17 + 18 + ... + 34)(35 + 36 + ... + 46) = 55082.
12 + 22 + 32 + 42 + ... + 462 = 33511, which consists of odd digits (the 3rd 5-digit sum).
467 = 435817657216, 43 + 581 + 765 + 721 + 6 = 462,
468 = 20047612231936,
2 + 0047 + 6 + 122 + 3 + 1936 = 2004 + 7 + 6 + 1 + 22 + 31 + 9 + 36
= 2004 + 7 + 61 + 2 + 23 + 1 + 9 + 3 + 6 = 2004 + 7 + 61 + 22 + 3 + 1 + 9 + 3 + 6
= 2004 + 76 + 1 + 2 + 2 + 3 + 19 + 3 + 6 = 2004 + 76 + 12 + 2 + 3 + 1 + 9 + 3 + 6 = 462,
469 = 922190162669056,
9 + 2 + 21 + 901 + 6 + 266 + 905 + 6 = 9 + 22 + 1 + 901 + 6 + 266 + 905 + 6
= 9 + 22 + 1901 + 6 + 26 + 6 + 90 + 56 = 9 + 221 + 901 + 6 + 2 + 66 + 905 + 6
= 9 + 221 + 901 + 62 + 6 + 6 + 905 + 6 = 92 + 2 + 1901 + 6 + 2 + 6 + 6 + 90 + 5 + 6
= 922 + 1 + 9 + 01 + 6 + 266 + 905 + 6 = 922 + 1 + 901 + 6 + 266 + 9 + 05 + 6 = 462.
Page of Squares : First Upload January 5, 2004 ; Last Revised January 27, 2011
by Yoshio Mimura, Kobe, Japan