When is it a prime?

Number Theory Level 3

Find the sum of all integers $n$ (positive or negative) such that $n^2-n$

is a prime .

1 solution

Muhammad Rasel Parvej
Dec 26, 2016

For any integer $n$ , $2 \mid n^2-n=n(n-1)$ .

So, $n^2-n$ is a prime only if $n^2-n=2 \implies n=2,-1$ .

For both $n=2$ and $n=-1$ , $n^2-n=2$ , a prime.

Hence, $2+(-1)=\boxed{1}$ is the answer.