Problem

Source: Ukrainian Mathematical Olympiad 2023. Day 1, Problem 11.1

Tags: number theory, Divisibility



Set $M$ contains $n \ge 2$ positive integers. It's known that for any two different $a, b \in M$, $a^2+1$ is divisible by $b$. What is the largest possible value of $n$? Proposed by Oleksiy Masalitin