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Let n be a-positive integer

  1. Jan 23, 2008 #1
    let n be a-positive integer. Prove that a and c leave the same remainder if and only if a - c =nk for some integer k.
     
  2. jcsd
  3. Jan 24, 2008 #2
    Suppose that

    [tex]\normalsize A=nQ_{1}+R_{1}[/tex]

    and

    [tex]\normalsize C=nQ_{2}+R_{2}[/tex]

    substract the two equation to get

    [tex]\normalsize A-C=n(Q_{1}-Q_{2})+(R_{1}-R_{2})[/tex]

    but the equation

    [tex]\normalsize A-C=n(Q_{1}-Q_{2})[/tex]

    requires that

    [tex]\normalsize R_{1}=R_{2}[/tex]

    Therefore the above result.
     
    Last edited: Jan 24, 2008
  4. Jan 24, 2008 #3
    Thank You
     
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