Question 32
Suppose a sequence $s_{1}, s_{2}, \ldots$, of positive integers satisfies $s_{n+2} = s_{n+1} + s_{n}$ for all positive integers $n$ (but not necessarily $s_{1} = s_{2} = 1$). Prove that there exists an integer $r$ such that $s_{n} - r$ is not divisible by $8$ for any integer $n$.