MathNet 2016-part-05 — 184 problems (EN–VI) Question 45

Let $n$ be a prime number. Show that there is a permutation $a_1, a_2, \dots, a_n$ of $1, 2, \dots, n$ so that $a_1, a_1a_2, \dots, a_1a_2 \dots a_n$ leave distinct remainders when divided by $n$.