Is there a sage module to solve equation such as ax+by=c?

Question

Is there a module in Sage to solve 2 unknowns in diophantine equations? For instance, ax+by=c where a,b,c are known

I tried basic extended euclidean algorithm but my numbers are too large.

Answer 1

Two ways of solving diophantine equations in Sage are

• using the Smith normal form of matrices over ZZ
• using polytopes

See the answers to these two Ask Sage questions:

• Ask Sage question 10364: Linear diophantine equations
• Ask Sage question 23666: Solving system of linear Diophantine equations