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
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
Publication date:
13.11.2022.
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