Show that there are infinitely many pairs of nonzero coprime integers a,b such that both quadratics x^2+ax+b=0 and x^2+2ax+b=0 have integral roots.

(In reply to Different sort of solution by Jer)

I've probably misunderstood your solution, but don't 2(s+t)=a and 4st=b have a common factor, 2, so that a,b are no longer coprime?

Posted by broll on 2022-04-01 23:10:35