Hi,

If I have the following equation

$\displaystyle 8x^2-4y^2=z$

and it is known that x and y are bothnon-equal,non-zero,evenintegers

then z will even and can be written $\displaystyle z=2u$

so that $\displaystyle 8x^2-4y^2=2u$

It is also required that z be a square integer

so it can be rewritten $\displaystyle z=2u=4v^2$

So with the above constraints I believe that

$\displaystyle 8x^2-4y^2=z$

can be rewritten

$\displaystyle 8x^2-4y^2=4v^2$

so

$\displaystyle 2x^2-y^2=v^2$

Have I made any fundamental mistakes anywhere?

Many thanks

Pro