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

Authors: SALAH EDDINE RIHANE, BERNADETTE FAYE, FLORIAN LUCA, ALAIN TOGBE

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

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