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m+n divides mn, then m + n <= n^2

Source: Tournament of Towns, Junior O-Level , Spring 2019 p3

May 9, 2020

number theoryTournament of TownsToTDivisibility

Problem Statement

The product of two positive integers

m

and

n

is divisible by their sum. Prove that

m + n \le n^2

.
(Boris Frenkin)