# Thread: problem finding a proof

1. ## problem finding a proof

i've been given this question as part of an assignment for a university maths subject.

"Prove that N squared minus 2 is never divisible by 3 if n is an integer"

any help anyone could give me on how to attack this proof would be great.

2. Originally Posted by bruxism
i've been given this question as part of an assignment for a university maths subject.

"Prove that N squared minus 2 is never divisible by 3 if n is an integer"

any help anyone could give me on how to attack this proof would be great.

N can take 3 forms by division algorithm:
3k,3k+1,3k+2

Check each one.

3. could you mayb elaborate just a little bit? It's only my first couple of weeks and i'm still trying to get my head around doing proofs. To me, writing proofs seems to be the mathematical thing i just can't get my head around.

4. Originally Posted by bruxism
could you mayb elaborate just a little bit? It's only my first couple of weeks and i'm still trying to get my head around doing proofs. To me, writing proofs seems to be the mathematical thing i just can't get my head around.
If N is divisible by 3 then N=3k, for some integer k, and N^2=9k^2,
so N^2-2=9k^2-2, which is not divisible by 3.

If N leaves remainder 1 when divided by 3 then N=3k+1, for some integer k,
and N^2=9k^2+6k+1, so N^2-2=9k^2+6k-1, which is not divisible by 3.

If N leaves remainder 2 when divided by 3 then N=3k+2, for some integer k,
and N^2=9k^2+12k+4, so N^2-2=9k^2+6k+2, which is not divisible by 3.

This exhausts all the possibilities of the remainder when N id divided by 3,
and in no case was N^2-2 divisible by 3, therefore for no N is N^2-2 divisible
by 3.

RonL