Question

Prove that n^4 +4 is a composite number for n>1.

Answer 1

If you worked on this for any length of time without success, you'll kick yourself now: n⁴ + 4 can be factored. Here it is:

n⁴ + 4
n⁴ + 4n² + 4 - 4n²
( n⁴ + 4n² + 4) - 4n²
((n² + 2) + 2n)((n² + 2) - 2n)

And since n>1 you can show that both factors are larger than one.
this shows it is composite when n is odd. If n is even it is clearly composite.