For example, 0 c + 1 r + 2 g = 10 turns into r = 10 – 2 g. Substitute that value for r in the other two equations and continue like this until you’ve defined all variables in terms of just one ...

We develop an algorithm for solving a system of diophantine equations with lower and upper bounds on the variables. The algorithm is based on lattice basis reduction. It first finds a short vector ...