Show that there exist no positive integers $\displaystyle m$ and $\displaystyle n$ such that $\displaystyle m^2+n^2$ and $\displaystyle m^2-n^2$ are both perfect squares.

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- Aug 23rd 2011, 04:33 AMalexmahoneShow that there exist no positive integers ...
Show that there exist no positive integers $\displaystyle m$ and $\displaystyle n$ such that $\displaystyle m^2+n^2$ and $\displaystyle m^2-n^2$ are both perfect squares.

- Aug 23rd 2011, 10:35 AMmeleseRe: Show that there exist no positive integers ...
There's a theorem by Fermat: The equation $\displaystyle x^4-y^4=z^2$ is not solvable in nonzero integers.

- Aug 23rd 2011, 04:49 PMalexmahoneRe: Show that there exist no positive integers ...