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

Authors : Salah Eddine RIHANE, Bernadette FAYE, Florian LUCA, Alain TOGBE

Pages : 1640-1649

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Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :In this paper, we find all the solutions of the title Diophantine equation in nonnegative integer variables $insert ignore into journalissuearticles values(m, n, x);$, where $P_k$ is the $k$th term of the Pell sequence.
Keywords : Pell numbers, linear form in logarithms, reduction method