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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Originally Posted by temp31415 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! i have proved this before but i can't find the thread.. anyways.. let . then for some integers x,y.. notice that, and , thus, .. so, .. hence,

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