2015 USAMO 第 5 题

Let $a, b, c, d, e$ be distinct positive integers such that $a^4 + b^4 = c^4 + d^4 = e^5$. Show that $ac + bd$ is a composite number.

令 $a、b、c、d、e$ 为不同的正整数，使得 $a^4 + b^4 = c^4 + d^4 = e^5$。证明 $ac + bd$ 是一个合数。