If gcd(ab,c) = 1 then gcd(a,c) = 1 and gcd(b,c) = 1

[iamalexalright]

Homework Statement

If gcd(ab,c) = 1 then gcd(a,c)=1 and gcd(b,c)=1


2. The attempt at a solution
Well, if gcd(ab,c) = 1 we know that

abk + cl = 1 for some integers k and l

not really sure where to go from here... any hints?

 

[Char. Limit]

Also, if gcd(a,c)=1, then am+cn=1 for some integers m and n. Now what if m=bk?

Repeat for the other one.

 

[iamalexalright]

oh wow, that is painfully obvious ... thanks Char. Limit !