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Math Help - Applying Euclid's Lemma to a problem

  1. #1
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    Applying Euclid's Lemma to a problem

    Hello there,

    I have a problem that i have troubles starting. I need to show if gcd(a, c)=1 and c divides ab, then c divides (ab + bx). My prof gave us a hint to use Euclid's lemma, which states if a divides bc and gcd(a, b) = 1 then a divides c.

    Edit: Ok, so i figured that, from Euclid's lemma we can get that c divides b, but now im stuck again

    Thank you in advance.
    Last edited by Lowoctave; November 8th 2011 at 06:15 PM.
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  2. #2
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    Re: Applying Euclid's Lemma to a problem

    if you've realized that c divides b, can you factor b out of your expression?
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  3. #3
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    Re: Applying Euclid's Lemma to a problem

    Wow.. i was looking for some hard trick.. it's so simple.. i feel like a fool heh..
    Thank you very much!

    God Bless!
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  4. #4
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    Re: Applying Euclid's Lemma to a problem

    oklets firstlyy c/ab & gcd(a.c)=1 so c/b then c/bx & c/ab
    finally c divise any linear combinaison between ab and bx
    so c/ab+cx ..
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