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gcd(a,b,c) = 1 , exists a so that gcd(p,q+ar) = 1

Source: KJMO 2014 p4

May 2, 2019
number theorygreatest common divisorpositive integers

Problem Statement

Positive integers p,q,rp, q, r satisfy gcd(a,b,c)=1gcd(a,b,c) = 1. Prove that there exists an integer aa such that gcd(p,q+ar)=1gcd(p,q+ar) = 1.
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