Writing It Up · Hard problem

A draft proof that $5 \nmid n^2 + n + 1$ reads: (A) every integer is $\equiv 0, 1, 2, 3$ or $4 \pmod 5$; (B) for $n \equiv 0, 1, 2$, $n^2 + n + 1 \equiv 1, 3, 2$; (C) for $n \equiv 3, 4$, $n^2 + n + 1 \equiv 3, 0$; (D) so $5 \nmid n^2 + n + 1$. Which line contains an error?