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Math Help - Basic proof

  1. #1
    Senior Member I-Think's Avatar
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    Basic proof

    Requesting proof verification, I detect a whiff of error in my proof

    Without using factorization of primes, show that is a,b,c\in{Z} and satisfy gcd(a,b)=1 and a|c and b|c, then ab|c

    If gcd(a,b)=1, then as+bt=1
    If a|c, am=c and if b|c, bn=c

    So c=c*1
    c=c*(as+bt)
    c=cas+cbt
    c=bnas+ambt
    c=ab(ns+mt)
    QED

    Is this proof 100% correct?
    Thanks for the help
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  2. #2
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    Quote Originally Posted by I-Think View Post
    Requesting proof verification, I detect a whiff of error in my proof

    Without using factorization of primes, show that is a,b,c\in{Z} and satisfy gcd(a,b)=1 and a|c and b|c, then ab|c

    If gcd(a,b)=1, then as+bt=1
    If a|c, am=c and if b|c, bn=c

    So c=c*1
    c=c*(as+bt)
    c=cas+cbt
    c=bnas+ambt
    c=ab(ns+mt)
    QED

    Is this proof 100% correct?
    Thanks for the help

    Yes, it is correct.

    Tonio
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