Question 83
Let $a_{n}$ be a sequence of natural numbers defined by $a_{1}=m$ and $a_{n}=a_{n-1}^{2}+1$ for $n \gt 1$. We call a pair $(a_{k}, a_{l})$ interesting if
(i) $0 \lt l-k \lt 2016$,
(ii) $a_{k}$ divides $a_{l}$.
Show that there exists an $m$ such that the sequence $a_{n}$ contains no interesting pair.
(i) $0 \lt l-k \lt 2016$,
(ii) $a_{k}$ divides $a_{l}$.
Show that there exists an $m$ such that the sequence $a_{n}$ contains no interesting pair.