MathNet 2022-part-04 — 197 problems (EN–VI) Question 100

Define $a_0 = 2$ and $a_{n+1} = a_n^2 + a_n - 1$ for $n \ge 0$. Prove that $a_n$ is coprime to $2n + 1$ for all $n \in \mathbb{N}$.