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Product of two elements is an element

Source: China Southeast Math Olympiad 2015 Day 2 P8

June 6, 2017
number theory

Problem Statement

For any integers m,nm,n, we have the set A(m,n)={x2+mx+n∣x∈Z}A(m,n) = \{ x^2+mx+n \mid x \in \mathbb{Z} \}, where Z\mathbb{Z} is the integer set. Does there exist three distinct elements a,b,ca,b,c which belong to A(m,n)A(m,n) and satisfy the equality a=bca=bc?
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