Question

If gcd(a,b)=1 then prove that gcd(ac,b)=gcd(c,b)

Answer 1

HINT: (a,b) = 1 means that there is some x and y such that ax + by = 1

Answer 2

perhaps start by writing \(d=gcd(ac,b)\) and \(e=gcd(b,c)\) and then show that \(d|e\) and \(e|d\)

Answer 3

How about this: http://math.stackexchange.com/questions/20889/

Answer 4

yes i guess that will do it. notice this fairly obvious fact actually takes a few lines to prove!

Answer 5

Yes, sat, it's one of the many things of number theory which are just intuitively plausible.

Answer 6

what do you mean @FoolForMath

Answer 7

If you see Sivaram's answer, he has used the same fact I alluded to you :)