MathNet 2003 — Part 02 Question 17

Let $x_{0}, x_{1}, x_{2}, \ldots$ be the sequence defined by $x_{0}=2$ and $x_{n+1}=5+\left(x_{n}\right)^{2}$ for each $n \geq 0$. Prove that no prime numbers other than 2 appear in this sequence.