# Thread: Basic proof

1. ## 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

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 $\displaystyle a,b,c\in{Z}$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