- #1

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## Homework Statement

Prove that if ##n^2## is divided by 3, then also n can also be divided by 3.

## Homework Equations

## The Attempt at a Solution

Is there anything wrong with this argument?

By contradiction, suppose ##3|n## and 3 doesn't divide ##n^2##.

Then ##3m = n##. Multiple both sides by ##n##

$$

3(mn) = n^2

$$

Thus, ##3|n^2## and we have reached a contradiction. Therefore, If ##3|n^2##, then ##3|n##.