ON SOLVING DIOPHANTINE EQUATIONS BY REAL MATRIX MANIPULATION

This note presents simple algorithms for obtaining the solutions of th e Diophantine equation. Our methods can produce classes of all solutio ns with lower degree than a specified number. The previous algorithms involve some troublesome computations, e.g., the calculation of both t he controllability indexes and the observability indexes or the soluti on of a pole assignment problem, etc.. Our contribution is that our al gorithm requires only basic matrix operations such as addition, subtra ction, multiplication, and inversion of given real matrices. In additi on, by solving simple linear equations, the class of all minimum degre e solutions can be given. Therefore tile computational efforts are red uced compared with previous algorithms.