Classical problems of Diophantus, Fermat and Ritt using New analytical and Algebraic Techniques

Diophantine equations are equations of the type f(x_1,..., x_n) = 0, where solutions have integral values. The function f is often a polynomial over the integers, but can also be of exponential type. The study of Diophantine equations (e.g. x^2 + y^2 = z^2) goes back to the Babylonians. Diophantus of Alexandria wrote a book on this topic. Even today there are many open problems, but also a large number of different methods to attack these problems. We intend to study several problems of this general Diophantine type from different view points. We expect that by sharing and combining the methods from both research groups (in Austria and Croatia), we can obtain considerably stronger results and we have encouraged your members of the research groups to take part.