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Correcting Proofs in a False Statement

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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 n^2 is not divisible by 3, then n is not divisible by 3.

Proof: If n^2 is not divisible by 3, then n^2 does not equal 3m for any integer m. Hence, n does equal 3l for any integer l. Therefore, n is not divisible by 3.

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In this solution, we walk the through how to correct proofs in a given false statement.

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We see that the first conditional statement in the proof is true, but we haven't made any initial assumption about (please see the attached file) and its divisibility by 3. We also still ...

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