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Math Help - Basic Number Theory

  1. #1
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    Basic Number Theory

    1. Is there such number N that 7 divided N^2=3?

    Isnt it just root of 7/3?


    2. x^2 + y^2 = z^2. Prove xyz is a multiple of 60



    Not sure what to do here, and where to get the xyz term from
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  2. #2
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    1)

    I assume you mean 7 divided by n^2 = 3

    If you're dealing with divisibility in number theory, I think the question may be asking if there is an integer which divides 7 giving the quotient 3. This would mean that 7 would have 3 as a factor. 7, being prime, has no factors.

    However the root of 7/3 does does yield a quotient of 3. The number does exist (root of 7/3), but it is not an integer.
    Last edited by jmedsy; November 2nd 2009 at 08:25 PM. Reason: further explain
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  3. #3
    MHF Contributor alexmahone's Avatar
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    Quote Originally Posted by Aquafina View Post
    1. Is there such number N that 7 divided N^2=3?

    Isnt it just root of 7/3?


    2. x^2 + y^2 = z^2. Prove xyz is a multiple of 60



    Not sure what to do here, and where to get the xyz term from
    2. x^2+y^2=z^2

    The solution set is (x, y, z)=(3k, 4k, 5k). xyz=60k^3. Thus xyz is a multiple of 60.
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  4. #4
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    Quote Originally Posted by alexmahone View Post
    2. x^2+y^2=z^2

    The solution set is (x, y, z)=(3k, 4k, 5k). xyz=60k^3. Thus xyz is a multiple of 60.
    so what about the set (5,12,13)?

    You've got to try the following:
    Prove that one of the numbers are divisble by 5,
    prove that one of them is divisible by 3
    and prove that one of them i divisible by 4.

    These statements are true and should not be to hard to prove.
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