We give the corresponding identities for different solutions of the equations: aA^{x}+bB^{x}=cD^{x} [1] and aA^{x}+bB^{y}=cD^{z }[2]: As for coprime integers a, b, c, A, B, D and arbitrary positive integers x, y, z further, for not coprime integers, if A_{0}^{x0}+B_{0}^{x0}=D_{0}^{xo }[3] and A_{0}^{x0}+B_{0}^{yo}=D_{0}^{z0 }[4], where x_{0}, y_{0}, z_{0}, A_{0}, B_{0}, D_{0} - are any solutions in positive integers.

Periodical:

Bulletin of Mathematical Sciences and Applications (Volume 5)

Pages:

44-47

Citation:

K. R. R. Gandhi and R. Tint, "The Proof of the Insolubility in Natural Numbers for n>2, the Fermat's Last Theorem and Beal's Conjecture for Co-Prime Integers Arranged in a Pair A, B, D in the Equations A^{n}+B^{n}=D^{n} and A^{n}+B^{y}=D^{z} (Elementary Aspect)", Bulletin of Mathematical Sciences and Applications, Vol. 5, pp. 44-47, 2013

Online since:

Aug 2013

Authors:

Distribution:

Open Access

This work is licensed under a

Creative Commons Attribution 4.0 International License

References:

PROF. DR. K. RAJA RAMA GANDHI, Reuven Tint The reproductive solution for Fermat, s Last theorem (elementary aspect)- first proof.

Reuven Tint, The Identities of Ordinary Which Is Leading to the Extraordinary Consequences (Elementary Aspect) Asian Journal of Mathematics and Applications - ISSN 2307-7743.

PROF. DR. K. RAJA RAMA GANDHI1 AND REUVEN TINT Proof of Beal's Conjecture.

pp.157-163, comments VII p.171).

Faltings G (1983). Endlichkeitssätze für abelsche Varietäten über Zahlkörpern,. Inventiones Mathematicae 73 (3): 349-366. doi: 10. 1007/BF01388432.

H. Davenport, The Higher Arithmetic, Moscow, (1965).