# 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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