Question 96
Let $m, n \geqslant 2$ be integers such that $\operatorname{gcd}(m, n)=\operatorname{gcd}(m, n-1)=1$. Define the sequence $\left(n_{k}\right)_{k \in \mathbb{N}}$ by $n_{0}=m$ and $n_{k+1}=n \cdot n_{k}+1$ for $k \in \mathbb{N}$. Prove that the integers $n_{1}, \ldots, n_{m-1}$ cannot all be prime numbers.