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Thread: 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 $\displaystyle a,b,c\in{Z} $and satisfy $\displaystyle gcd(a,b)=1$ and $\displaystyle a|c$ and $\displaystyle b|c$, then $\displaystyle ab|c$

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

    So $\displaystyle c=c*1$
    $\displaystyle c=c*(as+bt)$
    $\displaystyle c=cas+cbt$
    $\displaystyle c=bnas+ambt$
    $\displaystyle c=ab(ns+mt)$
    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 $\displaystyle a,b,c\in{Z} $and satisfy $\displaystyle gcd(a,b)=1$ and $\displaystyle a|c$ and $\displaystyle b|c$, then $\displaystyle ab|c$

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

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

    Is this proof 100% correct?
    Thanks for the help

    Yes, it is correct.

    Tonio
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