IJPAM: Volume 110, No. 4 (2016)

Title

ON A PARTICULAR DIOPHANTINE EQUATION

Authors

Carmine Boniello$^1$, Rosa Ferrentino$^2$
$^1$University of Salerno
Fisciano (Salerno) ITALY
$^2$Department of Economic and Statistics Sciences
University of Salerno
Fisciano (Salerno) Italy

Abstract

The aim of this paper is to present a result concerning the solutions of a particular Diophantine equation and that is to propose a simple and elementary algebraic proof of the fact that the Pythagorean triples, solution of the Diophantine equation $x^{2} +y^{2} =z^{2}$, $\forall \ x,y,z\in N$, do not satisfy a general Diophantine equation of the type $x^{n} +y^{n} =z^{n}$, $\forall\ x,y,z,n\in N$.

History

Received: August 2, 2016
Revised: November 8, 2016
Published: November 9, 2016

AMS Classification, Key Words

AMS Subject Classification: 11Y50, 11R04, 11D45
Key Words and Phrases: theory of numbers, pythagorean triples, diophantine equation

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How to Cite?

DOI: 10.12732/ijpam.v110i4.10 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 110
Issue: 4
Pages: 679 - 691


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