scholarly journals Beal Conjecture

2015 ◽  
Vol 14 ◽  
pp. 7-27
Author(s):  
Slobodan Stanojevic
Keyword(s):  
Number Theory ◽  
Fermat's Last Theorem ◽  
Fermat’S Last Theorem

Beal Conjecture was formulated in 1997 and presented as a generalization of Fermat's Last Theorem, within the field of number theory.

Fermat's Last Theorem. A Genetic Introduction to Algebraic Number Theory.

1978 ◽  
Vol 32 (143) ◽  
pp. 943
Author(s):  
Lawrence Washington ◽  
Harold M. Edwards
Keyword(s):  
Number Theory ◽  
Algebraic Number ◽  
Algebraic Number Theory ◽  
Fermat's Last Theorem ◽  
Fermat’S Last Theorem

What Does it Take to Prove Fermat's Last Theorem? Grothendieck and the Logic of Number Theory

2010 ◽  
Vol 16 (3) ◽  
pp. 359-377 ◽  
Author(s):  
Colin McLarty
Keyword(s):  
Number Theory ◽  
Fermat's Last Theorem ◽  
Fermat’S Last Theorem

AbstractThis paper explores the set theoretic assumptions used in the current published proof of Fermat's Last Theorem, how these assumptions figure in the methods Wiles uses, and the currently known prospects for a proof using weaker assumptions.

scholarly journals On the Rationality and Transcendentality of Solutions to the Equation x^n + y^n = z^n

2019 ◽  
Author(s):  
Binh Ho
Keyword(s):  
Number Theory ◽  
Transcendental Number ◽  
Fermat's Last Theorem ◽  
Fermat’S Last Theorem

In this paper, the author develops 2 theorems that serve as extensions to the well-known Fermat’s Last Theorem in the field of number theory. The first proposed theorem in this paper states that if there exist numbers x, y, and an integer z such that x^n + y^n = z^n for any integer n > 2, then both/either x and/or y must be irrational. The second proposed theorem in this paper states that if there exist a number x, a transcendental number y, and an integer z such that x^n + y^n = z^n for any integer n > 2, then x must be irrational. The proposed theorems in this paper expand on the notion that if there exist numbers x, y, and an integer z such that x^n + y^n = z^n for any integer n > 2, then at least x or y is not an integer, which is stated in Fermat’s Last Theorem.

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