SCHWEITZER 2015 Problem 4

Let $a_n$ be a series of positive integers with $a_1=1$ and for any arbitrary prime number $p$ , the set $\{a_1,a_2,\cdots,a_p\}$ is a complete remainder system modulo $p$ . Prove that $\lim_{n\rightarrow \infty} \cfrac{a_n}{n}=1$ .