An elementary proof of Catalan-Mihailescu theorem

Jamel Ghannouchi (1)

1 ESSTT - Ecole Supérieure des Sciences et Techniques [Tunis]

More than one century after its formulation by the Belgian mathematician Eugene Catalan, Preda Mihailescu has solved the open problem. But, is it all ? Mihailescu's solution utilizes computation on machines, we propose here not really a proof as it is entended classically, but a resolution of an equation like the resolution of the polynomial equations of third and fourth degrees. This solution is totally algebraic and does not utilize, of course, computers or any kind of calculation. We generalize our approach to Pillai and Fermat-Catalan equations and discuss the solutions.

Mots clés: Algebraic resolution; Diophantine equations; Catalan equation

Domaines: Mathématiques générales [math.GM]

Jamel Ghannouchi. An elementary proof of Catalan-Mihailescu theorem. 2011. ⟨hal-00677731v35⟩