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3m + n = 3u + d , where u =lcm (m,n) and d=gcd(m,n) , prove n | m

Source: 2002 Estonia National Olympiad Final Round grade 10 p1

March 16, 2020
GCDLCMdivisibledividesnumber theory

Problem Statement

The greatest common divisor dd and the least common multiple uu of positive integers mm and nn satisfy the equality 3m+n=3u+d3m + n = 3u + d. Prove that mm is divisible by nn.
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