Proof for the Beal conjecture and a new proof for Fermat's last theorem

摘要

The Beal Conjecture was formulated in 1997 and presented as a generalization of Fermat's Last Theorem, within the number theory's field. It states that, for X, Y, Z, n, n_1 and n_2 positive integers with n_1, n_2, n_3> 2, if X~(n_1) + Y~(n_2) = Z~(n_3) then X, Y, Z must have a common prime factor. This article presents the proof for the Beal Conjecture, obtained from the correspondences between the real solutions of the equations in the forms A~2 + B~2 = C~2, δ~n + γ~n = α~n and X~(n_1) + Y~(n_2) = Z~(N_3) . In addition, a proof for the Fermat's Last Theorem was performed using basic math.