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Math Help - Bezout's Identity and Properties of Division

  1. #1
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    Bezout's Identity and Properties of Division

    I need to write a proof for class and I'm having a lot of trouble getting started. Maybe someone here can help me.

    Problem:

    Let a,m,n be integers and d=gcd(m,n). If m divides an and d divides a, then m divides a2.
    (Is there a way to use LaTeX on this forum?)

    My Thoughts:

    I know we must use Bezout's Identity to solve this. So far I have that since d=gcd(m,n) and d|a, there exist integers r and s such that mr + ns = a.
    That is all I have, and I really cannot for the life of me see what I'm supposed to do next. Does anybody see where I need to go from here?
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  2. #2
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    Re: Bezout's Identity and Properties of Division

    it looks like you're almost there:

    consider amr + ans = a2.

    clearly m|amr and m|ans, since m|m, and m|an, thus m divides their sum.
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