Yep you can do that with the fundamental theorem of arithmetic. Assume does not appear in the decomposition of Then...Contradiction seems straightforward
I'm asked to prove this lemma using the fundamental theorem of arithmetic:
Suppose and is prime. If then or .
I understand how to prove this using normal methods. (Contradiction seems straightforward.) However, I've read the definition of the fundamental theorem of arithmetic on wikipedia, and am stuck on how to use it to prove the statement.