Question 131
Let $p$ be a prime number. Prove that it is possible to choose a permutation $a_{1}, a_{2}, \ldots, a_{p}$ of $1,2, \ldots, p$ such that the numbers $a_{1}, a_{1} a_{2}, a_{1} a_{2} a_{3}, \ldots, a_{1} a_{2} a_{3} \cdots a_{p}$ all leave different remainders upon division by $p$.