Diophantine equation of second degree $x^2+y^2+z^2=2t^2$ How to solve this Diophantine equation of second degree? 
Solution, references, anything. I will be very grateful. 

$$x^2+y^2+z^2=2t^2$$

Thank you.
You can start with $x,y,z$ any Pythagorean triple, then take $t=z$.  There are more.
For every $t$, $x^2+y^2+z^2=2t^2$, defines a 3-Dimensional sphere with radius $\sqrt{2}t$. Thus, every point on the surface of the sphere is a solution for the diophantine equation. If you are interested in characterizing all the solutions, this should help
\begin{align}
r&amp;=\sqrt{2}t \\
x&amp;=r\sin{(\theta)}\cos(\phi) \\
y&amp;=r\sin{(\theta)}\sin(\phi) \\
z&amp;=r\cos{(\theta)} \\
\end{align} 
where $0\leq \theta \leq \pi$ and $0 \leq \phi \leq 2\pi$. Thus, substituting any value for $t$ , $\theta$ and $\phi$ in the above mentioned equations will give you a solution.