# Thread: Another question

1. ## Another question

if group G=Z, show aZ+bZ=gcd(a,b)Z.

I know gcd(a,b)=ax+by and aZ=<a> where <a>={a^n} but where to go from there i'm stuck

Some help will be greatly appreciated

2. Originally Posted by tamiani
if group G=Z, show aZ+bZ=gcd(a,b)Z.

I know gcd(a,b)=ax+by and aZ=<a> where <a>={a^n} but where to go from there i'm stuck

Some help will be greatly appreciated
To show $\left< a, b\right> = \left< d \right>$ where $d$ is a greatest common divisor you need to show: (i)if $x\in \left< a,b\right>$ then $x\in \left< d\right>$, (ii)if $x\in \left< d \right>$ then $x\in \left< a\right>$.