Question 6
Let $(x_n)$ be defined by $x_0=2$, $x_1=1$ and $x_{n+2}=x_{n+1}+x_n$ for all $n\ge0$.
(a) For $n\ge1$, prove that if $x_n$ is prime, then either $n$ is prime or $n$ has no odd prime divisor.
(b) Find all pairs of nonnegative integers $(m,n)$ such that $x_n$ is divisible by $x_m$.
(a) For $n\ge1$, prove that if $x_n$ is prime, then either $n$ is prime or $n$ has no odd prime divisor.
(b) Find all pairs of nonnegative integers $(m,n)$ such that $x_n$ is divisible by $x_m$.