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Math Help - factors

  1. #1
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    factors

    2n^2=m^2

    Why is 2 a factor of m?
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  2. #2
    MHF Contributor Unknown008's Avatar
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    Put this into this form:

    m^2 = 2n^2 = 2 \times n \times n

    It is like factorising a number.

    You can divide m^2 by 2 without getting a remainder, but a quotient equal to n^2.

    I hope it helps.
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  3. #3
    MHF Contributor undefined's Avatar
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    Quote Originally Posted by Stuck Man View Post
    2n^2=m^2

    Why is 2 a factor of m?
    So, m and n are integers.

    If m^2 is twice n^2 that means m^2 is even. (Which is the same as saying 2 is a factor of m^2.) But if m^2 is even then m must also be even.

    As it turns out, we know something stronger: that 4 is a factor of m.

    Are you looking at a proof that the square root of 2 is irrational, by chance?
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  4. #4
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    Yes good guess.
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  5. #5
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    if m is even say 2k for some integer k, then m^2=(2k)^2=4k^2 and so m^2 is even.

    if m is odd say 2k+1 for some integer k, then m^2=(2k+1)^2=4k^2+4k+1 is odd.

    so if 2 divides m^2, then m^2 is even and by above m is even and so 2 divides m.
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  6. #6
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    This has been more complicated than I first thought. Wikipedia has the full proof which was useful.
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