Show that: $\displaystyle c\mid ab \Rightarrow c\mid (a,b).(b,c)$

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(a,b)=gcd(a,b)

(b,c)=gcd(b,c)

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- Dec 15th 2008, 09:48 PMSeaDivisibility (gcd)
Show that: $\displaystyle c\mid ab \Rightarrow c\mid (a,b).(b,c)$

______________________________________________

(a,b)=gcd(a,b)

(b,c)=gcd(b,c) - Dec 15th 2008, 11:40 PMo_O
Are you sure that's the correct statement?

For example, $\displaystyle 6 \mid (8 \times 9)$ but $\displaystyle (8,9) \cdot (9,6) = (1)(3) = 3$ and $\displaystyle 6 \not{\mid} \ 3$