[46.2] Let $a_{1}, a_{2}, \cdots$ be a sequence of integers, where there are infinitely many positive integers and infinitely many negative integers. Prove: If for every positive integer $n$, the integers $a_{1}, a_{2}, \cdots, a_{n}$ yield distinct remainders when divided by $n$, then each integer appears exactly once in the sequence $a_{1}, a_{2}, \cdots$.