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BMSA > BMSA Volume 5 > The Proof of the Insolubility in Natural Numbers...
The Proof of the Insolubility in Natural Numbers for n&gt;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<sup>n</sup>+B<sup>n</sup>=D<sup>n</sup> and A<sup>n</sup>+B<sup>y</sup>=D<sup>z</sup> (Elementary Aspect)
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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 An+Bn=Dn and An+By=Dz (Elementary Aspect)

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Abstract:

We give the corresponding identities for different solutions of the equations: aAx+bBx=cDx [1] and aAx+bBy=cDz [2]: As for coprime integers a, b, c, A, B, D and arbitrary positive integers x, y, z further, for not coprime integers, if A0x0+B0x0=D0xo [3] and A0x0+B0yo=D0z0 [4], where x0, y0, z0, A0, B0, D0 - are any solutions in positive integers.

Info:

Periodical:
Bulletin of Mathematical Sciences and Applications (Volume 5)
Pages:
44-47
DOI:
https://doi.org/10.18052/www.scipress.com/BMSA.5.44
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 An+Bn=Dn and An+By=Dz (Elementary Aspect)", Bulletin of Mathematical Sciences and Applications, Vol. 5, pp. 44-47, 2013
Online since:
August 2013
Authors:
K. Raja Rama Gandhi, Reuven Tint
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Open Access

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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).

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