Saunderson found a parametric solution giving Euler bricks:
Let $(x,y,z)$ be a pythagoran triple, then we get an Euler brick $(a,b,c)$ with $a=x(4y^2-z^2)$, $b=y(4x^2-z^2)$, $c=4xyz$.
It is claimed, that the parametric solution is not giving all possible Euler bricks- but why? (https://mathworld.wolfram.com/EulerBrick.html)
Can you think of any example? And maybe a proof why that example is not given by the parametric solution?