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

**dwsmith** · October 9th 2010, 03:35 PM

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?

**Jhevon** · October 9th 2010, 03:39 PM

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

**mathdigger** · October 9th 2010, 07:16 PM

@dwsmith:
The fault with your argument is that you don't know whether kj/m would come out to be an integer or not.

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