I am trying to solve the following form of linear Diophantine equation: ax + by + cz = d

Having previously looked at two variable Diophantine equations (ax + bx = c), I have learnt to apply the Euclidean algorithm to find an initial solution and then to find other solutions through the general solution.

I have successfully applied the Euclidean algorithm to three-variable equations to find an initial solution, however I was unable to prove any general formulas I came up with to find more solutions.

Does anyone know if there is a standard general formula that can be used for three-variable Diophantine equations?


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.