\( n^4 + 4 = (n^2-2n+2)(n+2n+2)\) So the expression \( n^4+4\) can be factored for every \(n > 1\) and hence it can never be a prime for \(n>1\)
–
Vikram Waradpande
·
4 years ago

Log in to reply

@Vikram Waradpande
–
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.
–
Tim Vermeulen
·
4 years ago

## Comments

Sort by:

TopNewest\( n^4 + 4 = (n^2-2n+2)(n+2n+2)\) So the expression \( n^4+4\) can be factored for every \(n > 1\) and hence it can never be a prime for \(n>1\) – Vikram Waradpande · 4 years ago

Log in to reply

– Tim Vermeulen · 4 years 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.Log in to reply

– Vikram Waradpande · 4 years ago

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