When are a and x whole integers in 3(x²)=a²?

[W3pcq]

3(x^2)=a^2

When are a and x whole integers?

 

[HallsofIvy]

In what sense does this have anything to do with "Tensor Analysis and Differential geometry"? I'm moving it to "number theory".

In any case, if 3x²= a² for a and x integers, then we must have
$a= x\sqrt{3}$ which is impossible unless x= a= 0. It implies $\sqrt{3}= a/x$ but $\sqrt{3}$ is irrational.

The only integer solution to 3x²= a² is x= a= 0.