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infinite triples a,b,c such a+b +c=n, ax^2 + bx + c = 0 has rational roots

Source: Lusophon 2019 CPLP P2

December 31, 2019
algebratrinomialRational roots

Problem Statement

Prove that for every nn nonzero integer , there are infinite triples of nonzero integers a,ba, b and cc that satisfy the conditions: 1. a+b+c=na + b + c = n 2. ax2+bx+c=0ax^2 + bx + c = 0 has rational roots.
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