Salvage of a divisibility proposition.

Problem:

"Determine the sufficient (and if possible necessary) conditions on an integer n for the following statement to be true: "For integers a and b, if n doesn't divide ab, then n doesn't divide a and n doesn't divide b." Then state the condition on n and the resulting implication as a proposition and prove it"

I was able to work out something that makes sense to me, but considering I didn't put a specific condition on n, I was wondering if I might have made a mistake.

Attempted proof:

"Assume that n, a, and b are integers such that n doesn't divide ab. Since n doesn't divide ab, by definition ab does not equal kn, where k is some integer. Because ab does not equal kn, neither a nor b can be multiples of n, otherwise ab would produce another multiple of n, which n would divide. Because a does not equal kn and b does not equal kn, n doesn't divide a and n doesn't divide b respectively."