How to Prove: If 3 divides n^2, then 3 divides n.

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This video shows how to prove that if 3 divides n^3, then 3 divides n.

I hope that you will find it helpful.
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Would you recommend shortening some working here by using some modular arithmetic? Like:
Assume n ≡ 1(mod 3) or 2 (mod 3)
n² ≡ 1 (mod 3) only since 1² = 1 ≡ 1(mod 3) and 2² = 4 ≡ 1(mod 3)
Proven by contrapositive.

Also how would you generalise this to all primes? Since obviously for some arbitrarily big prime you cannot go case by case like this.
Good video by the way, been meaning to get into more number theory :)

squeezy
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And right when I thought I escaped arithmetics they come to me

elliotthedoge