A Deeper Analysis on a Generalization of Fermat¡äs Last Theorem

Leandro Torres Di Gregorio

Journal of Mathematics Research, 2018, vol. 10, issue 2, 1-23

Abstract: In 1997, the following conjecture was considered by Mauldin as a generalization of Fermat's Last Theorem: ¡°for X, Y, Z, n$_1$, n$_2$ and n$_3$ 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¡±. The present work provides an investigation focusing in various aspects of this conjecture, exploring the problem¡äs specificities with graphic resources and offering a complementary approach to the arguments presented in our previous paper. In fact, we recently discovered the general form of the counterexamples of this conjecture, what is explored in detail in this article. We also analyzed the domain in which the conjecture is valid, defined the situations in which it could fail and previewed some characteristics of its exceptions, in an analytical way.

Keywords: diophantine equations; Fermat¡äs Last Theorem; Beal conjecture; Tijdeman-Zagier conjecture (search for similar items in EconPapers)
Date: 2018
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.ccsenet.org/journal/index.php/jmr/article/view/72655/40336 (application/pdf)
http://www.ccsenet.org/journal/index.php/jmr/article/view/72655 (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:ibn:jmrjnl:v:10:y:2018:i:2:p:1

Access Statistics for this article

More articles in Journal of Mathematics Research from Canadian Center of Science and Education Contact information at EDIRC.
Bibliographic data for series maintained by Canadian Center of Science and Education ().