Algorithmic Number Theory

Volume 4076 of the series Lecture Notes in Computer Science pp 182-192

Use of Extended Euclidean Algorithm in Solving a System of Linear Diophantine Equations with Bounded Variables

  • Parthasarathy RamachandranAffiliated withIndian Institute of Science


We develop an algorithm to generate the set of all solutions to a system of linear Diophantine equations with lower and upper bounds on the variables. The algorithm is based on the Euclid’s algorithm for computing the GCD of rational numbers. We make use of the ability to parametrise the set of all solutions to a linear Diophantine equation in two variables with a single parameter. The bounds on the variables are translated to bounds on the parameter. This is used progressively by reducing a n variable problem into a two variable problem. Computational experiments indicate that for a given number of variables the running times decreases with the increase in the number of equations in the system.