It's a fun (and not too hard) puzzle to find disjoint sets {A1,A2,A3,...,An} and {B1,B2,B3,...,Bn} of integers with equal 0th, 1st, 2nd,..., (k-1)th moments with n = 2^(k-1). (Maybe someone already mentioned that in this thread, but I didn't see it.) Jim Propp On Tue, Feb 21, 2012 at 6:54 PM, Warren Smith <warren.wds@gmail.com> wrote:
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)
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