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Math Help - Relationships via modulo arithmetic.

  1. #1
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    Relationships via modulo arithmetic.

    Please assist me in solving this question. Thanks.
    Attached Thumbnails Attached Thumbnails Relationships via modulo arithmetic.-question.png  
    Last edited by mr fantastic; October 15th 2011 at 09:43 PM. Reason: Re-titled.
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  2. #2
    MHF Contributor alexmahone's Avatar
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    Re: Relationships via modulo arithmetic.

    i) If 5 | x - y and 7 | x - y, then 35 | x - y.

    ii) Symmetric: If x\equiv y \pmod{35},

    y\equiv x \pmod{35}

    Transitive: If x\equiv y \pmod{35} and y\equiv z \pmod{35},

    Adding, we get

    x\equiv z \pmod{35}
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  3. #3
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    Re: Relationships via modulo arithmetic.

    Quote Originally Posted by alexmahone View Post
    i) If 5 | x - y and 7 | x - y, then 35 | x - y.

    ii) Symmetric: If x\equiv y \pmod{35},

    y\equiv x \pmod{35}

    Transitive: If x\equiv y \pmod{35} and y\equiv z \pmod{35},

    Adding, we get

    x\equiv z \pmod{35}
    note that (i) holds only because gcd(5,7) = 1.
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