On the exponential Diophantine equation $P_n^x+P_{n+1}^x=P_m$

Authors

SALAH EDDINE RIHANE
BERNADETTE FAYE
FLORIAN LUCA
ALAIN TOGBE

DOI

10.3906/mat-1810-130

Abstract

In this paper, we find all the solutions of the title Diophantine equation in nonnegative integer variables $(m, n, x)$, where $P_k$ is the $k$th term of the Pell sequence.

Keywords

Pell numbers, linear form in logarithms, reduction method

First Page

1640

Last Page

1649

Recommended Citation

RIHANE, SALAH EDDINE; FAYE, BERNADETTE; LUCA, FLORIAN; and TOGBE, ALAIN (2019) "On the exponential Diophantine equation $P_n^x+P_{n+1}^x=P_m$," Turkish Journal of Mathematics: Vol. 43: No. 3, Article 39. https://doi.org/10.3906/mat-1810-130
Available at: https://journals.tubitak.gov.tr/math/vol43/iss3/39