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gcm and lcm

Source: Netherlands Team Selection Test 2016 Day 1-Problem 3

September 22, 2016
number theoryleast common multiple

Problem Statement

Find all positive integers kk for which the equation: lcm(m,n)−gcd(m,n)=k(m−n) \text{lcm}(m,n)-\text{gcd}(m,n)=k(m-n) has no solution in integers positive (m,n)(m,n) with m≠nm\neq n.
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