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x^2 +ax+b=y^2+cy+d has infinitely integer solutions iff a^2 -4b = c^2 - 4d

Source: Brazilian Mathematical Olympiad 1985 P4

July 27, 2018
Diophantine equationnumber theorytrinomialIntegers

Problem Statement

a,b,c,da, b, c, d are integers. Show that x2+ax+b=y2+cy+dx^2 + ax + b = y^2 + cy + d has infinitely many integer solutions iff a2−4b=c2−4da^2 - 4b = c^2 - 4d.
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