Proving that gcd(a,b) = 1 when am + bn = 1

[CarmineCortez]

Homework Statement

if am + bn = 1 m,n integers then gcd(a,b) = 1 a,b natural

Homework Equations

i don't know where to start.

The Attempt at a Solution

 

[jhicks]

Say gcd(a,b)=p where p is a natural number > 1. Can am+bn=1? Remember that gcd(a,b)=p means a and b have a common factor of p so they can be written as say a=x*p and b=y*p for some integers x and y.

 

[Hurkyl]

i don't know where to start.

Definitions are almost always a good place to start. Checking for similar problems in your textbook is another good one. You should never be at a complete loss as to how to begin a problem.