How do you prove that (n^4) +4 is composite for all n>1 ?(adsbygoogle = window.adsbygoogle || []).push({});

I found this problem in a book I was reading. The even n part is obvious. The proof for odd n cannot be done by trying to factorize [(2k+1)^4]+4. I know this is true, because I've tried and moreover, the factors of the first few such numbers are : (2*2*5),(5*17),(2*2*5*13),(17*37),(2*2*5*5*13),(5*13*37),... The expected factors of 4 appear in the even numbers, but the factors for the odds seem patternless. So, I imagine that the proof must be done by some other means.

Any ideas ?

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# (n^4) + 4 is composite ?

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