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Mathematical Proof =\?
Prove that for all integers n, if 3 divides n(squared) then 3 divides n.
I attempted this problem but am not sure that it is correct. This is my solution:
If 3 divides n, then n = 3a.
n(squared) = (3a)(squared)
n(squared) = 9a(squared)
3 divides 9a(squared)
Therefore if 3 divides n(squared) then 3 divides n.
I am no good at proofs but that is the only thing i could come up with. Thanks for any help!
1 Answer
- doug_donaghueLv 71 decade agoFavourite answer
You've 'kinda' got the right idea, but you went after it kinda 'backwards'. What you've proven is that, if 3|n (the | means 'divides exactly' with no remainder) then 3|n² which is kinda trivial.
If p factors into q*r, then a|p => either a|q or a|r. Therefore, if 3|n² then 3|n or 3|n and the proof is complete.
You really, *really* need to get after understanding proofs. They are at the absolute heart of all of mathematics.
HTH ☺
Doug
