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Find maximum of m+n if lcm(m,n) = (m-n)^2

Source: Iran First Round 2017, P17

March 7, 2021
number theoryleast common multiple

Problem Statement

Two positive integers mm and nn are both less than 500500 and lcm(m,n)=(māˆ’n)2\text{lcm}(m,n) = (m-n)^2. What is the maximum possible value of m+nm+n?
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