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On two AP

Source: Iranian Our MO 2020 P5

March 11, 2020
Arithmetic Progressionnumber theory

Problem Statement

Concider two sequences xn=an+bx_n=an+b, yn=cn+dy_n=cn+d where a,b,c,da,b,c,d are natural numbers and gcd(a,b)=gcd(c,d)=1gcd(a,b)=gcd(c,d)=1, prove that there exist infinite nn such that xnx_n, yny_n are both square-free.
Proposed by Siavash Rahimi Shateranloo, Matin Yadollahi Rated 3
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