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Possible Duplicate:
Iterated polynomial problem

Let $P(x)$ be a polynomial with integer coefficients. For each positive integer $P(n)>n$. Consider the sequence defined by $x_1=1$ and $x_{k+1}=P(x_k)$ for $k>1$. For each positive integer $n$, there exist a member of the sequence that is divisible by $n$. Prove that $P(n)=n+1$ for each positive integer $n$.

I got that $x_2=2$. Let $P(x)=a_nx^n+...+a_1x+a_0$. If $x_2>2$ then it's easy to prove with induction that for all positive integers $k$, $x_k\equiv 1\mod x_2-1$ by looking at the coefficients. This implies that no number in the sequence is divisble by $x_2-1$. I'm stuck here.

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    @HaraldHanche-Olsen , iran tst 2$0$042013-12-05

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