I have been studying group theory for some time now, and I have noted that quite a few theorems/proofs considering finite groups rely on results from number theory, a branch of mathematics of which I have very little knowledge.
One question that I would like to have answered concerns the divisors of a product of integers.
Let m and n be integers. Is it true (and can you prove/disprove) that the divisors of mn are either divisors of m, divisors of n or common multiples of m and n?
In particular, is it true that the divisors of mp with p a prime number are either multiples of p or divisors of m?