Is it true that for any polynomial $P$ of degree $\geq 1$ with coefficients in $\mathbb{N}$, and any positive integer $a$, the sequence defined by $a_0=a,$ $a_{n+1}=P(a_n)$ contains infinitely many composite numbers?
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2You might want to show some of your work or your thoughts about the question. Also, some context about the problem would be nice. It would help users in giving an answer appropriate to your experience and skill. – user0 Sep 12 '18 at 14:52
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Please tell us what led you to your question? Without more context, it reads like an exercise you're stuck on, which asked you to prove one way or the other, whether your conjecture is true. – amWhy Dec 16 '22 at 22:04