21 Feb
2012
21 Feb
'12
8:52 p.m.
an example I just found: {-241,-218,0,0,+218,+241}, {-266,-143,-120,+120,+143,+266} Are two multisets of 6 integers each with same sums of Jth powers for J=0,1,2,3,4,5. Note 0^4 + 218^4 + 241^4 = 5631933137 = 120^4 + 143^4 + 266^4 0^2 + 218^2 + 241^2 = 105605 = 120^2 + 143^2 + 266^2 and the sums of 1st and 3rd powers of course are 0 by odd symmetry. Prouhet–Tarry–Escott problem... thanks for that name... is the same problem except they demand sets not multisets ("multi"sets allow repeating an element): http://en.wikipedia.org/wiki/Prouhet–Tarry–Escott_problem