Prove there are no positive natural solutions to the system of equations: $X^2+Y^2=Z^2$ and $Z^2+Y^2=V^2$.
I've tried several techniques and gotten little progress. I do not know what to do.
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1Welcome to the stack exchange! Can you explain what you have tried so far? – LostStatistician18 Apr 13 '22 at 02:01
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1Your first equation can be rewritten as $Z^2 - Y^2 = X^2$, so along with $Z^2 + Y^2 = V^2$, note that a duplicate would then be There don't exist $a, b$ positive integers such that $a^2 + b^2$ and $a^2 - b^2$ are perfect squares. Also note this was found using Approach0. – John Omielan Apr 13 '22 at 02:23