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Another NT with GCD and LCM

Source: INAMO 2023 P5 (OSN 2023)

August 30, 2023
number theorygreatest common divisorleast common multipleIndonesiaIndonesia MO

Problem Statement

Let aa and bb be positive integers such that gcd(a,b)+lcm(a,b)\text{gcd}(a, b) + \text{lcm}(a, b) is a multiple of a+1a+1. If b≤ab \le a, show that bb is a perfect square.
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