## If $p=i+1, r\in \mathbb{Z}[i]$, $f=x^n-r$ is reducible in $\mathbb{Z}[i][x]$ and $p|r$ then $2|r$

If $$p=i+1, r\in \mathbb{Z}[i]$$, $$f(x)=x^n-r$$ is reducible in $$\mathbb{Z}[i][x]$$ and $$p|r$$ then $$2|r$$.

I know that Norm$$(p) = 2$$ and since $$f$$ is reducible we get $$f(x) = g_1(x)\cdots g_k(x)$$ into linear factors. But from here I don’t know where to go.