Is there a complete answer to this problem? I have found Saunderson's answer, but I believe it is missing a few answers. The problem states:
$a^2+b^2=d^2 \\ a^2+c^2=e^2 \\ b^2+c^2=f^2$
Saunderson proves the answer is
$a=y(4x^2-z^2)\\ b=x(4y^2-z^2)\\ c=4xyz$
where $x,y,z$ is the Pythagorean triple $x^2+y^2=z^2$. But this skips answers like $(85,132,720)$,$(132,351,720)$, etc.
The complete Saunderson proof is here: https://play.google.com/books/reader?id=1NI_AQAAMAAJ&printsec=frontcover&output=reader&hl=en&pg=GBS.PA429
The solutions are also known as Euler Bricks.
Also (since I don't think a complete answer exists), do any of you have suggestions on how to find one?