2 problems

Let $a,b,c\in\mathbb{Z}\setminus\{0\}$ and $d\in\mathbb{Z}$. Consider the Diophantine equation … The integers $X_1,X_2,X_3,X_4$ are co-prime when their greatest common divisor is…

Let $F\in\mathbb{Z}[x,y,z]$ be a quadratic form, and consider the Diophantine equation … where $G$ is the polynomial defined in the source by equation. A solution $(x,y,z)$ is prim…