Hi,

Can anyone show that $\displaystyle 4a^4+8a^3 b-12ab^3-7b^4$ can be a perfect square if a and b are integers and a > b > 0 ?

I think that $\displaystyle a(a+2b)$ and $\displaystyle b(12a+7b)$ must simultaneously be squares but am struggling to get further

got further

can $\displaystyle 48(a-b)+7$ be a perfect square?