**AMC 10 Mock Exam Question 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 $1$?

$\displaystyle\textbf{(A) } \frac{1}{5}\qquad\textbf{(B) } \frac{2}{5}\qquad\textbf{(C) } \frac{3}{5}\qquad\textbf{(D) } \frac{4}{5}\qquad\textbf{(E) } 1$

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