TITLE: free group generated by polynomials
QUESTION [5 upvotes]: Someone recently asked me how to proof that $x+1$ and $x^3$ generate a free group. A colleague has worked out a proof. I have a vague memory that this has been studied, maybe a Monthly problem? Does anyone know any history on this? 
Edit: Sorry for my omission of key point. The group operation here is function composition on the reals, or the integers. Each of the polynomials can be viewed as a permutation of Z = all integers (or on the reals). Viewed in that way, do they generate a free group (of rank two).

REPLY [6 votes]: This is a question asked by Harvey Friedman (I don't know where and when) and which was first solved by Samuel White in 1988, The group generated by $x \mapsto x + 1$ and $x \mapsto x^p$ is free, Journal of Algebra, Volume 118, Issue 2, 1 November 1988, Pages 408–422.
There's an earlier incomplete solution by Zassenhaus in On a problem by Harvey Friedman Communications in Algebra, Volume 6, Issue 16, 1978.
You can find further references in item II.40 of de la Harpe's book Topics in Geometric Group theory.