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Thread: if (a,b)=1 and (b,c)=1, then (a,c)=1

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    if (a,b)=1 and (b,c)=1, then (a,c)=1

    if $\displaystyle (a,b)=1$ and $\displaystyle (b,c)=1$, then $\displaystyle (a,c)=1$

    So $\displaystyle 1|a, \ 1|b, \ 1|c$

    How can I show $\displaystyle 1=gcd(a,c)$??
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    Re: if (a,b)=1 and (b,c)=1, then (a,c)=1

    Quote Originally Posted by dwsmith View Post
    if $\displaystyle (a,b)=1$ and $\displaystyle (b,c)=1$, then $\displaystyle (a,c)=1$
    So $\displaystyle 1|a, \ 1|b, \ 1|c$
    How can I show $\displaystyle 1=gcd(a,c)$??
    Consider $\displaystyle (9,8)=1,~(8,3)=1~\&~(9,3)=3~.$
    Is is the it true?
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