Question 80
$p \neq 13$ is a prime number in the form of $8k + 5$ for some natural number $k$, and $39$ is a non-residue modulo $p$. Prove that equation $x_1^4 + x_2^4 + x_3^4 + x_4^4 \equiv 0 \pmod{p}$ has a solution in the set of integers such that $p \nmid x_1x_2x_3x_4$.