Question 67
Suppose that for a prime number $p$ and integers $a$, $b$, $c$ the following holds:
$$
6 \mid p + 1, \quad p \mid a + b + c, \quad p \mid a^4 + b^4 + c^4.
$$
Prove that $p \mid a$, $b$, $c$.
$$
6 \mid p + 1, \quad p \mid a + b + c, \quad p \mid a^4 + b^4 + c^4.
$$
Prove that $p \mid a$, $b$, $c$.