Could anyone assist me with this problem...

"Use mathematical induction to prove the following generalization.

Suppose are integers and p is a prime number. If , then for some ." [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.