Show that if g.c.d.(x,y) = g.c.d.(x,z) = 1 then g.c.d.(x,yz) = 1
One important fact:
- If and and , then
Basically, any common divisor of two numbers will divide the gcd of those two numbers.
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Let .
Multiply both sides by :
Since and , then . (Why?)
But this means and which implies because of .
But . Can you conclude?