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.

DOI

10.3906/mat-1810-130

Keywords

Pell numbers, linear form in logarithms, reduction method

First Page

1640

Last Page

1649

Recommended Citation

RIHANE, S. E, FAYE, B, LUCA, F, & TOGBE, A (2019). On the exponential Diophantine equation $P_n^x+P_{n+1}^x=P_m$. Turkish Journal of Mathematics 43 (3): 1640-1649. https://doi.org/10.3906/mat-1810-130

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