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Set With a^2+1 Divisible by b

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

April 5, 2023
number theoryDivisibility

Problem Statement

Set MM contains n≥2n \ge 2 positive integers. It's known that for any two different a,b∈Ma, b \in M, a2+1a^2+1 is divisible by bb. What is the largest possible value of nn?
Proposed by Oleksiy Masalitin
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