(though the Stone-Weiestrauss theorem applies, I don't think this is adequate
to do the analysis with polynomial approximations instead, though it would be
nice if it did).
The only answer is the trivial answer .
Follow, ecMathGeek's approach and arrive at:
Hence, is the only possible constant.
This problem was taken from my math book, which said it appeared as a problem in the 1990 Putnam. The problem I posed was a variation of that problem, not exactly the same.