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sapiental
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Homework Statement
Prove the following: If the integer n is divisible by 3 then n^3 is divisible by 3.
Homework Equations
Direct Proof
The Attempt at a Solution
n = 3m
n^2 = 9m^2
n^2 = 3(3m^2)
I think the proof is done at this point because the 3 factors out but I also did this:
n^2 = 9m^2
(n^2)/9 = m^2
(n/3)(n/3) = (m)(m)
which also implies n is divisible by 3 since integer x integer = integer
My professor is kind of harsh on proofs so I am not sure if there are intermediate steps I'm missing. Thanks!