1. The problem statement, all variables and given/known data Suppose that gcd(a, b) = 1 with a, b > 0, and let x0, y0 be any integer solution to the equation ax + by = c. Find a necessary and sufficient condition, possibly depending on a, b, c, x0, y0 that the equation have a solution with x > 0 and y > 0. 2. Relevant equations 3. The attempt at a solution I'm pretty lost. Can anyone point me in the right direction?