TY - JOUR
T1 - A Proof of Bealâ€™s Conjecture
AU - Ghanouchi, Jamel
JF - Bulletin of Mathematical Sciences and Applications
VL - 5
SP - 30
EP - 34
SN - 2278-9634
PY - 2013
PB - SciPress Ltd
DO - 10.18052/www.scipress.com/BMSA.5.30
UR - https://www.scipress.com/BMSA.5.30
AB - 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 of Catalan theorem 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).
ER -