Number Theory- Mathematical Proof I am trying to prove a theorem in my textbook using another theorem. What I need to show  that 
if a,b, and c are positive integers, show that the least positive integer linear combination of a and b equals the least positive integer linear combination of a+cb and b. 
Any help would be great, I am new at proving things in mathematics. 

Let the least positive linear combination of $a,b$ be $f$.  You can write $f=da+eb$  Now show you can write $f$ as a linear combination of $a+cb, b$. You should be able to find explicit coefficients for the combination.  To show this is minimum, assume you can write $g \lt f$ as a linear combination of $a+cb, b$.  Show you can write $g$ as a linear combination of $a,b$ violating the assumption that $f$ is the minimum positive combination.
