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Number theory

Source: RMM 2018 D2 P4

February 25, 2018
number theory

Problem Statement

Let a,b,c,da,b,c,d be positive integers such that ad≠bcad \neq bc and gcd(a,b,c,d)=1gcd(a,b,c,d)=1. Let SS be the set of values attained by gcd⁡(an+b,cn+d)\gcd(an+b,cn+d) as nn runs through the positive integers. Show that SS is the set of all positive divisors of some positive integer.
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