Mathematics and Applied Mathematics
July 13, 2013
The Pillai’s conjecture states that there is finite number of solutions for perfect powers separated by a number. 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 Beal equation and discuss the solutions. (Keywords : Diophantine equations, Catalan, Fermat-Catalan, Conjectures, Proofs, Algebraic resolution).