[hal-00677731] An elementary proof of Catalan-Mihailescu theorem

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



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