Equations and implication

by Nattasha   Last Updated September 23, 2018 14:20 PM

There are two equations: $x^2 − px + q = 0$ and $x^2 − px − q = 0$,

$p$, $q$ are natural numbers. Prove that if both equations have integer roots, then there are natural numbers $a$, $b$, such that $p^2=a^2+b^2$ .

Is converse implication true?



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