Prime numbers and dynamics of the polynomial $x^2-1$

Ivan Penkov, Michael Stoll

Let $n\in {\mathbb{Z}}_{⩾2}$. By $P(n)$ we denote the set of all prime divisors of the integers in the sequence $n,n^2-1,(n^2-1{)}^2-1,\dots$. We ask whether the set $P(n)…