Question 93
Let $n$ be a positive integer and let $a, b, c, d$ be integers such that $n|a + b + c + d$ and $n|a^2 + b^2 + c^2 + d^2$. Show that
$$
n|a^4 + b^4 + c^4 + d^4 + 4abcd.
$$
$$
n|a^4 + b^4 + c^4 + d^4 + 4abcd.
$$
MathNet 2016-part-01 — 184 problems (EN–VI) Question 93
Math Olympiad Vault · MathNet 2016-part-01 — 184 problems (EN–VI)