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Math Help - Running Through Positive Divisors

  1. #1
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    Running Through Positive Divisors

    Hi there! This is my first post!

    I am confused over what is means to run through the divisors. The question is:

    Show that if n>0, then as d runs through the positive divisors of n, so does n/d.

    Thanks for your help!
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by KatyCar View Post
    Hi there! This is my first post!

    I am confused over what is means to run through the divisors. The question is:

    Show that if n>0, then as d runs through the positive divisors of n, so does n/d.

    Thanks for your help!
    What does "run through" mean?
    Last edited by Drexel28; February 3rd 2010 at 07:02 PM.
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  3. #3
    MHF Contributor Bruno J.'s Avatar
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    It's an expression used in many number theory texts, which essentially means : "as d takes on all possible values of divisors of n, so does n/d".
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    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by Bruno J. View Post
    It's an expression used in many number theory texts, which essentially means : "as d takes on all possible values of divisors of n, so does n/d".
    Isn't the question fairly trivial then...
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  5. #5
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    The question most likely has a very simple solution

    Unfortunately I am not familiar with number theory as I have just decided to start studying it so I do not see the solution.

    If someone wouldn't mind giving a little more of an explanation it would me most helpful. Thanks!
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  6. #6
    MHF Contributor Bruno J.'s Avatar
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    Well consider the set of all pairs (d, n/d) where d is a divisor of n. What you want to show is that every divisor d occurs not only as a first element of some pair (which it does by definition) but also as the second element of some pair. Hint : show that when d is a divisor of n, d'=n/d is also a divisor of n. Which pair has d' as a first element?
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