The smallest squares containing k 43's :
4356 = 662, 4343056 = 20842, 5434343524 = 737182,
39434343224329 = 62796772, 26434343643243561 = 1625864192.
43 is the sum of m squares for m = 3, 4, ..., 29.
432 is the second square which is the sum of 7 fifth powers : 25 + 25 + 25 + 35 + 35 + 35 + 45.
432 = 1849, its digits being distinct. A zigzag square.
12 + 152 + 292 + 432 = 542.
The sum of consecutive odd primes is 432.
438 = 11688200277601, 1 + 1688 + 20 + 02 + 77 + 60 + 1 = 432.
Komachi equations:
432 = 1 + 2 * 3 * 4 * 56 + 7 * 8 * 9 = - 1 - 23 + 45 * 6 * 7 - 8 - 9,
432 = - 9 - 87 + 6 * 54 * 3 * 2 + 1 = - 98 + 7 * 6 * 54 - 321,
432 = 9 * 8 * 7 + 65 + 4 * 32 * 10 = 98 + 7 + 6 + 54 * 32 + 10
432 = - 98 - 7 + 6 * 54 * 3 * 2 + 10 = - 98 - 7 + 654 * 3 + 2 - 10,
432 = 92 * 82 + 72 - 62 - 542 + 32 - 212 = 92 + 82 + 72 * 62 - 52 - 42 * 32 / 22 + 12
= 92 - 82 + 72 - 62 - 52 + 432 - 22 - 12 = 92 - 82 - 72 * 62 + 52 * 42 * 32 - 22 * 12
= 92 - 82 - 72 * 62 + 52 * 42 * 32 - 22 / 12.
(432 + 1) = (62 + 1)(72 + 1) = (22 + 1)(32 + 1)(62 + 1),
(432 + 7) = (12 + 7)(152 + 7).
1582 = 202 + 212 + 222 + ... + 432.
(1)(2 + 3 + ... + 19)(20 + 21 + ... + 43) = 3782,
(1 + 2 + ... + 6)(7 + 8 + ... + 14)(15 + 16 + ... + 43) = 12182,
(1 + 2 + ... + 6)(7 + 8 + ... + 19)(20 + 21 + ... + 43) = 16382,
(1 + 2 + ... + 8)(9 + 10 + ... + 36)(37 + 38 + ... + 43) = 25202,
(1 + 2 + ... + 15)(16 + 17 + ... + 19)(20 + 21 + ... + 43) = 25202,
(1 + 2 + ... + 23)(24 + 25)(26 + 27 + ... + 43) = 28982,
(1 + 2 + ... + 35)(36)(37 + 38 + ... + 43) = 25202.
(12 + 22 + ... + 42)(52 + 62 + ... + 122)(132 + 142 + ... + 432) = 223202,
(12 + 22 + ... + 72)(82 + 92 + 102)(112 + 122 + ... + 422)(432) = 12642002.
Page of Squares : First Upload December 22, 2003 ; Last Revised May 21, 2010
by Yoshio Mimura, Kobe, Japan