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Math Help - proof that n is a multiple of 6

  1. #1
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    proof that n is a multiple of 6

    ok im completely stumped with this with the equation
    n = m^3 - m
    for when n & m are integers
    how to you show that n is a multiple of 6?
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  2. #2
    MHF Contributor alexmahone's Avatar
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    Quote Originally Posted by renlok View Post
    ok im completely stumped with this with the equation
    n = m^3 - m
    for when n & m are integers
    how to you show that n is a multiple of 6?
    n=m^3-m

    n=m(m^2-1)

    n=m(m+1)(m-1)

    m(m+1)(m-1) is the product of 3 consecutive integers. So one of the factors is a multiple of 3 and one of the factors is a multiple of 2.

    So m(m+1)(m-1) is a multiple of 6.

    n is a multiple of 6.
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