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Math Help - problem finding a proof

  1. #1
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    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.

    Thanks heaps in advance.
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  2. #2
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    Quote Originally Posted by bruxism View Post
    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.

    Thanks heaps in advance.
    N can take 3 forms by division algorithm:
    3k,3k+1,3k+2

    Check each one.
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  3. #3
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    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.
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  4. #4
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    Quote Originally Posted by bruxism View Post
    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
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