On the exponential Diophantine equation Px n + P x n+1 + ⋯ + P x n+k-1 = Pm-Reference-Cited by-同舟云学术

On the exponential Diophantine equation Px n + P x n+1 + ⋯ + P x n+k-1 = Pm

Published:2020-12-01 Issue:6 Volume:70 Page:1333-1348
ISSN:1337-2211
Container-title:Mathematica Slovaca
language:en
Short-container-title:

Author:

Luca Florian¹²³⁴,Tchammou Euloge⁵,Togbé Alain⁶

Affiliation:

1. School of Mathematics , University of the Witwatersrand , Private Bag X3, Wits , Johannesburg , South Africa

2. Research Group in Algebraic Structures and Applications , King Abdulaziz University , Jeddah , Saudi Arabia

3. Max Planck Institute for Mathematics , Bonn , Germany

4. Centro de Ciencias Matemáticas UNAM , Morelia , Mexico

5. Institut de Mathématiques et de Sciences Physiques , Dangbo , Bénin

6. Department of Mathematics , Statistics and Computer Science , Purdue University Northwest, 1401 S, U.S. 421 , Westville , IN , USA

Abstract

Abstract In this paper, we find all the solutions of the title Diophantine equation in positive integers (m, n, k, x), where P i is the i th term of the Pell sequence.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/ms-2017-0435/pdf

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