Find four distinct positive integers such that the sum of any three of them is a perfect square.

{{1,32,88,136},{1,34,65,190},{1,44,124,316},{1,44,124,316},{2,37,130,157},{2,41,78,281},{2,57,110,617},{3,34,63,159},{4,41,76,244},{4,57,108,564},{4,68,97,124},{5,34,61,130},{6,39,99,151},{6,41,74,209},{6,57,106,513},{7,34,59,103},{8,41,72,176},{8,57,104,464},{9,34,57,78},{9,46,114,201},{10,41,70,145},{10,57,102,417},{12,41,68,116},{12,57,100,372},{14,41,66,89},{14,57,98,329},{16,57,96,288},{18,57,94,249},{20,57,92,212},{22,57,90,177},{24,57,88,144},{26,57,86,113}}

It got much easier as I got smarter about the hunt. I think these are all the quads that have a triplet adding to 13^2 or lower. I'll wait for the CS crew for a definitive list to compare too.

Cool problem!

Posted by owl on 2005-02-23 21:35:31