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

Bernadette Faye, Carlos Gomez, Florian Luca, Salah Rihane, Alain Togbe


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 $k$th term of the Pell sequence.


Pell numbers, Linear forms in logarithms, reduction methods

Full Text:


ISSN: 1331-0623 (Print), 1848-8013 (Online)