1. ## 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

2. 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