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Mar31-09, 11:52 PM
P: 29
Wow, quite a coincidence - I just read chapter 3 of Stillwell, "Mathematics and Its History", which mentions this result! He says it was proved by Cauchy in 1813, with a "short" proof by Nathanson in 1987 (Proc Am Math Soc, 99, 22-24).

good luck!