[math-fun] sets of integers with equal moments?

Your task is to find two disjoint sets (or multisets) {A1,A2,A3,...,Ak} and {B1,B2,B3,...,Bk} of integers with equal 0th, 1th, 2th,..., (k-1)th moments. k=1: {x} and {y} work, trivial. k=2: {0,0} and {-x,+x} have equal sums of Jth powers for J=0 and 1. k=4: {-5,0,0,+5} and {-4,-3,+3,+4} have equal sums of Jth powers for J=0,1,2,3. Also any pythagorean triple works instead of 3,4,5. k=6: ?I do not know of any example? -- Warren D. Smith http://RangeVoting.org  <-- add your endorsement (by clicking "endorse" as 1st step)