The Diophantine equations P-n(x)+ P-n+1(y) = P-m(x) or P-n(y) + P-n+1(x) = P-m(x)

Bernadette Faye; Florian Luca; Salah Eddine Rihane; Alain Togbe

doi:10.1007/s13398-023-01425-7

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The Diophantine equations P-n(x)+ P-n+1(y) = P-m(x) or P-n(y) + P-n+1(x) = P-m(x)

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The Diophantine equations P-n(x)+ P-n+1(y) = P-m(x) or P-n(y) + P-n+1(x) = P-m(x)

Bernadette Faye, Florian Luca, Salah Eddine Rihane and Alain Togbe

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas, Vol.117(2)

01/04/2023

DOI: https://doi.org/10.1007/s13398-023-01425-7

Abstract

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Here, we find all positive integer solutions of the Diophantine equations in the title, where (P-n)(n=0) is the Pell sequence P-0 = 0, P-1 = 1 and Pn+2 = 2P(n+1) + P-n for all n = 0.

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Title: The Diophantine equations P-n(x)+ P-n+1(y) = P-m(x) or P-n(y) + P-n+1(x) = P-m(x)
Creators - without role: Bernadette Faye - Université Gaston Berger
Florian Luca - University of the Witwatersrand
Salah Eddine Rihane - Supreme Council Of Health
Alain Togbe - Purdue University Northwest
Publication Details: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas, Vol.117(2)
Publisher: Springer Nature
Number of pages: 13
Identifiers: 9939827408331
Academic Unit: King Abdulaziz University
Language: English
Resource Type: Journal article