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Original scientific paper

Complete solution of the exponential Diophantine equation \(P_n^x+P_{n+1}^x=P_m^y\)

Bernadette Faye ; UFR SAT, Section Maths Appliquees, University Gaston Berger of Saint-Louis (UBG), Saint-Louis, Senegal
Carlos Gomez ; Departamento de Matematicas, Universidad del Valle, Cali, Colombia
Florian Luca ; School of Mathematics, University of the Witwatersrand, Johannesburg, South Africa
Salah Rihane ; National Higher School of Mathematics, Sidi Abdallah, Algiers, Algeria
Alain Togbe ; Department of Mathematics and Statistics, Purdue University Northwest, Westville , USA


Full text: english pdf 181 Kb

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Abstract

In this paper, we find all the solutions of the title Diophantine equation in positive integer variables (m, n, x,y), where \(P_k\) is the kth term of the Pell sequence.

Keywords

Pell numbers, Linear forms in logarithms, reduction methods

Hrčak ID:

285102

URI

https://hrcak.srce.hr/285102

Publication date:

13.11.2022.

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