Could anyone assist me with this problem...

"Use mathematical induction to prove the following generalization.

Suppose $\displaystyle a_1, a_2, ..., a_n$ are integers and p is a prime number. If $\displaystyle p|a_1 a_2 ... a_n$, then $\displaystyle p|a_i$ for some $\displaystyle i = 1, 2, ..., n$." [Hint: The induction step has two cases.]

I believe I can use this theorem without proof:

Suppose a and b are integers and p is a prime number. if p|ab, then p|a or p|b. This theorem comes from the uniqueness of prime factorization section.