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  1. #1
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    If n squared is a multiple of 3...

    If n squared is a multiple of 3 must n be a multiple of 3?

    My approach was to assume n is not a multiple of three and so is of the form 3k+1, 3k+2, then squaring shows that n squared is not a multiple of three, but I am just not sure if this establishes the converse, does it?
    Last edited by mr fantastic; September 13th 2010 at 01:33 PM. Reason: Copied title into main body of post.
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  2. #2
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    Quote Originally Posted by berachia View Post
    ...must n be a multiple of 3?

    My approach was to assume n is not a multiple of three and so is of the form 3k+1, 3k+2, then squaring shows that n squared is not a multiple of three, but I am just not sure if this establishes the converse, does it?
    You actually proved the contrapositive, which is equivalent to what you were asked to prove in the first place.
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  3. #3
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    Try proving a more general result - if p|ab => p|a OR p|b. Where p is prime and a,b are any integers.
    Above will follow directly from this.
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