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Serbia national Olympiad Day 1 problem 2

Source: Serbia national Olympiad Day 1 problem 2

March 28, 2015
number theoryTST

Problem Statement

Let kk be fixed positive integer . Let Fk(n)Fk(n) be smallest positive integer bigger than knkn such that Fk(n)āˆ—nFk(n)*n is a perfect square . Prove that if Fk(n)=Fk(m)Fk(n)=Fk(m) than m=nm=n.
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