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  1. #1
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    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
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  2. #2
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    Quote Originally Posted by tamiani View Post
    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 $\displaystyle \left< a, b\right> = \left< d \right>$ where $\displaystyle d$ is a greatest common divisor you need to show: (i)if $\displaystyle x\in \left< a,b\right>$ then $\displaystyle x\in \left< d\right>$, (ii)if $\displaystyle x\in \left< d \right>$ then $\displaystyle x\in \left< a\right>$.
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