Question: Show that (ma,mb) = m(a,b) if m if greater than 0.

Answer: c = (a,b)

c = xa + yb

mc = mxa + myb = m(a,b)

This is where I'm stuck, I'm not sure how to prove that m(a,b) = (ma,mb). I also know that mc|ma and mc|mb.

Thanks!

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- Dec 10th 2007, 06:38 PMtemp31415gcd question
Question: Show that (ma,mb) = m(a,b) if m if greater than 0.

Answer: c = (a,b)

c = xa + yb

mc = mxa + myb = m(a,b)

This is where I'm stuck, I'm not sure how to prove that m(a,b) = (ma,mb). I also know that mc|ma and mc|mb.

Thanks! - Dec 11th 2007, 05:22 AMkalagota
i have proved this before but i can't find the thread.. anyways..

let $\displaystyle d = (ma,mb)$. then $\displaystyle d = max + may$ for some integers x,y..

notice that, $\displaystyle m|max$ and $\displaystyle m|may$, thus, $\displaystyle m|d$..

so, $\displaystyle \frac{d}{m} = ax + by$.. hence, $\displaystyle \frac{d}{m} = (a,b) \implies d = m(a,b)$