Basic proof

**I-Think** · October 25th 2010, 04:38 PM

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

**tonio** · October 25th 2010, 08:26 PM

Originally Posted by I-Think

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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