Let $\displaystyle p$ be an odd prime and let $\displaystyle a_1, . . . ,a_{p-1}\$ be a permutation of $\displaystyle \{1, 2, . . ., p-1\}$. Prove that there exist $\displaystyle i \not = j$ such that $\displaystyle ia_i\equiv ja_j(\bmod p)$.

How can I use Wilson's theorem to prove this. I appreciate any help.