Question 23
N6 (LAT) Let $x_1$ and $x_2$ be relatively prime positive integers. For $n\ge2$, define $x_{n+1}=x_nx_{n-1}+1$.
(a) Prove that for every $i\gt 1$, there exists $j\gt i$ such that $x_i^i$ divides $x_j^j$.
(b) Is it true that $x_1$ must divide $x_j^j$ for some $j\gt 1$?
(a) Prove that for every $i\gt 1$, there exists $j\gt i$ such that $x_i^i$ divides $x_j^j$.
(b) Is it true that $x_1$ must divide $x_j^j$ for some $j\gt 1$?