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composite number criterion, exist a,b,x,y \in N+ : a+b = n , x/a + y/b= 1

Source: 1997 Estonia National Olympiad Final Round grade 11 p1

March 11, 2020
number theoryCompositeprime

Problem Statement

Prove that a positive integer nn is composite if and only if there exist positive integers a,b,x,ya,b,x,y such that a+b=na+b = n and xa+yb=1\frac{x}{a}+\frac{y}{b}= 1.
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