# Prove that

n^4+4 prime number <==> n=1

4 years, 11 months ago

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$$n^4 + 4 = (n^2-2n+2)(n+2n+2)$$ So the expression $$n^4+4$$ can be factored for every $$n > 1$$ and hence it can never be a prime for $$n>1$$

- 4 years, 11 months ago

That's not complete, you should mention that $$n^2-2n+2=1 \implies (n-1)^2=0 \implies n = 1$$, and if $$n>1$$, then both factors are bigger than $$1$$, hence $$n^4+4$$ is not prime.

- 4 years, 11 months ago

Oh yeah, forgot that! That's why you're on level 5 and i'm on 4!

- 4 years, 11 months ago