A proof of Pillai conjecture

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. Then, we generalize the proof to Pillai conjecture.

Mots clés: Diophantine equations; Catalan equation; Pillai conjecture; Algebraic resolution

Domaines: Mathématiques générales [math.GM]

Jamel Ghannouchi. A proof of Pillai conjecture. 2012. ⟨hal-00698687v22⟩