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Math Help - gcd proof 1

  1. #1
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    gcd proof 1

    let a,b,c belongs to integers.prove that the equation ax+by=c has integer solutions if and only if (a,b)|c.
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by Deepu View Post
    let a,b,c belongs to integers.prove that the equation ax+by=c has integer solutions if and only if (a,b)|c.
    This is a number theory proof. If ax+by=c then we have that (a,b)\mid ax,by\implies (a,b)\mid ax+by=c. Try the other way.
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  3. #3
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    Quote Originally Posted by Drexel28 View Post
    This is a number theory proof. If ax+by=c then we have that (a,b)\mid ax,by\implies (a,b)\mid ax+by=c. Try the other way.
    Thank you... but can you do this proof by the concept of division algorithm method..
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  4. #4
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by Deepu View Post
    Thank you... but can you do this proof by the concept of division algorithm method..
    No. Can you?
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