Linear Diophantine Equations Solver
Linear Diophantine Equations are of the form ax + by = c where the solutions (x, y) are integers.

Approach
There exists a standard algorithm to find any one solution of the Diophantine equation. This solution can then be transposed to yield all infinite solutions to the equation. This algorithm exploits the well-known Extended Euclidean Algorithm

Resources
For further information, please see :

1. CP Algorithms Article
2. Wikipedia Article on Extended Euclidean Algorithm
3. Wikipedia Article On Linear Diophantine Equations