Resumen de Consideraciones en torno a ecuaciones diofánticas no lineales

Jesús Álvarez Mesa

• It is known an algebraic equation with n variables has real or complex solutions, which will depend on n-1 parameters. Assuming explicit solutions exist, non-linear two-or-three-variable algebraic equations are solved in this work. In order to do so, certain algebraic conditions are imposed on the initial parametric equations so as to find all the rational solutions. Thus, an already estudied Diophantine problem is completely solved. Finally, an attempt to justify the fact of other non-linear equations lacking rational solutions is carried out.