Correcting proofs in a false statement

Question

Assignment:

Not every error in a proof is a false statement.  Sometimes every line is true, but the lines don't directly follow the previous lines.  All that's needed to fix the error is more detail or explanation.  Explain where the error is in the following proof and then fix it.

Prove:   If n² is not divisible by 3, then n is not divisible by 3.

Proof:   If n² is not divisible by 3, then n² does not equal 3m for any integer m.  Hence, n does equal 3l for any integer l.  Therefore, n is not divisible by 3.

Provide complete and step by step solution for the question and show calculations and use formulas.