- #1

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- 11

## Homework Statement

if 1 = gcd(a,b), show that gcd(ac,b) = gcd(c,b)

## Homework Equations

None

## The Attempt at a Solution

My attempt at a solution:

Let d = gcd(ac,b),

Let g = gcd(c,b),

I want to show that g|d and that d|g. I then went on to make a bunch of circular writing and get nowhere... I set up things like:

1 = ax + by

d = acw + bz --> 1 = (ac/d)w + (b/d)z

g = cn + bm --> 1 = (c/d)n + (b/d)m

Is my approach here a solid method? I can't think of any other way to show that gcd(ac,b) = gcd(c,b) besides assigning each of them a value and showing that they divide each other.