Define a0=2 and an+1=a2n+an−1 for n≥0. Prove that an is coprime to 2n+1 for all n∈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 a0=2 and an+1=a2n+an−1 for n≥0. Prove that an is coprime to 2n+1 for all n∈N.