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…

Euler's conjecture. The roots of a fifth-degree equation should be expressible in the form