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Prove Divisibility

  1. Sep 30, 2003 #1
    Hello,

    I am supposed to prove or disprove this statement:

    Let m,d,n,a be non-zero integers. If m = dn, and if m|an, then d|a.


    I had a proof but I made an error. Stay tuned for my revised proof.




    Ok! Here is my corrected proof:


    By definition:

    An integer "a", is a divisor/factor of an integer "b" if

    b = ax for some integer x.


    If "m" is a divisor of "an" then there must be an x such that

    an = mx for some integer x.


    If m = dn then

    an = dnx for some integer x.


    By laws of cancellation,

    a = dx for some integer x.


    Therefore by definition, "d" is a divisor of "a" since

    a = dx for some integer x.

    Is this an adequate proof? If adequate, is there anything I can do to make this proof better? Any input is appreciated. Thankyou.
     
    Last edited by a moderator: Sep 30, 2003
  2. jcsd
  3. Sep 30, 2003 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Looks like a good proof to me.

    I'm impressed!
     
  4. Sep 30, 2003 #3
    Thanks for checking it out Ivy. I really appreciate it.

    I know it's a pretty Mickey Mouse proof, but it is pretty satisfying to come up with a correct proof by oneself.

    Now onto more proofs.



    Cheers.
     
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