- #1

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!