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Feb 1, 2011 at 15:15 comment added Chulumba @Scott, thanks. I did not consider cases. So, that's one step ahead and makes the would-be solutions more interesting. @Igor, that's a good suggestion. I will try to find polynomial counterexamples.
Jan 31, 2011 at 7:25 comment added Igor Rivin @Scott: I suspect there are polynomial counterexamples for the "other cases", but have been too lazy to program this.
Jan 31, 2011 at 3:03 comment added S. Carnahan @Chulumba: This is pretty easy to prove by induction for the case when the constant terms of $f$ and/or $g$ are nonzero. I do not know how to do it for other cases.
Jan 30, 2011 at 6:22 comment added Chulumba How, sir? I do not see how you determined equality to be the only solution class.
Jan 30, 2011 at 4:41 history answered Igor Rivin CC BY-SA 2.5