Using Primes and Local Analysis

If $k$ is odd, then prove that $$1+2+\ldots+n|1^k+2^k+\ldots+n^k$$

Let $a,b,c,d,e$ be distinct positive integers satisfying $$a^4+b^4=c^4+d^4=e^5.$$ Show that $ac+bd$ and $ad+bc$ are both composite numbers.

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