AMC 10 2017b Problem 14

An integer $N$ is selected at random in the range $1\leq N \leq 2020$ . What is the probability that the remainder when $N^{16}$ is divided by $5$ is $1$? $\textbf{(A)}\ \frac{1}{5} \textbf{(B)}\ \frac{2}{5} \textbf{(C)}\ \frac{3}{5} \textbf{(D)}\ \frac{4}{5} \textbf{(E)}\ 1$