Define $a_0 = 2$ and $a_{n+1} = a^2_n + a_n -1$ for $n \ge 0$. Prove that $a_n$ is coprime to $2n + 1$ for all $n \in N$.
Problem
Source: 2022 Saudi Arabia November Camp Test 2.1 BMO + EGMO TST
Tags: recurrence relation, Recurrence, number theory
Source: 2022 Saudi Arabia November Camp Test 2.1 BMO + EGMO TST
Tags: recurrence relation, Recurrence, number theory
Define $a_0 = 2$ and $a_{n+1} = a^2_n + a_n -1$ for $n \ge 0$. Prove that $a_n$ is coprime to $2n + 1$ for all $n \in N$.