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Math Help - GCD Proof

  1. #1
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    GCD Proof

    Let a, b, c be integers. If gcd(a, b) = 1 and c | (a+b), show that gcd(a, c) = 1.

    >>If gcd(a, b) = 1, then (a+b) shares no common factors with a or b, besides 1.
    For this reason, c, a factor of (a+b), cannot share any common factors with a or b, besides 1.
    Thus, gcd(a, c) = 1.


    That is how I figured this proof, but I'm worried I'll lose marks for not throughly explaining how the >>ed line is true. Try as I might, I haven't thought of a good way of proving it. I came to that conclusion inherently, but I know it's right...Any hints to a way in proving it?

    Also, my apologies if this is the wrong forum, I wasn't sure if this question was tough enough to get into the other algebra forum.
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by BlackBlaze View Post
    Let a, b, c be integers. If gcd(a, b) = 1 and c | (a+b), show that gcd(a, c) = 1.

    >>If gcd(a, b) = 1, then (a+b) shares no common factors with a or b, besides 1.
    For this reason, c, a factor of (a+b), cannot share any common factors with a or b, besides 1.
    Thus, gcd(a, c) = 1.


    That is how I figured this proof, but I'm worried I'll lose marks for not throughly explaining how the >>ed line is true. Try as I might, I haven't thought of a good way of proving it. I came to that conclusion inherently, but I know it's right...Any hints to a way in proving it?

    Also, my apologies if this is the wrong forum, I wasn't sure if this question was tough enough to get into the other algebra forum.
    this is in the wrong forum. see here

    ask questions there if you need clarification. i am going to close this thread since it is the same question
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