# a|m and b|m does that mean a*b|m?

• Oct 9th 2010, 03:35 PM
dwsmith
a|m and b|m does that mean a*b|m?
If a|m and b|m, does that mean a*b|m?

ak=m
bj=m
$akbj=m^2$
$ab(kj)=m^2\rightarrow ab \left(\frac{kj}{m}\right)=m$

Is this how it would be shown?
• Oct 9th 2010, 03:39 PM
Jhevon
Quote:

Originally Posted by dwsmith
If a|m and b|m, does that mean a*b|m?

ak=m
bj=m
$akbj=m^2$
$ab(kj)=m^2\rightarrow ab left(\frac{kj}{m}\right)=m$

Is this how it would be shown?

Shown? It's not true. Take a = 2, and b = m = 4
• Oct 9th 2010, 07:16 PM
mathdigger
@dwsmith:
The fault with your argument is that you don't know whether kj/m would come out to be an integer or not.