- Turkish Journal of Mathematics
- Vol: 43 Issue: 3
- On the exponential Diophantine equation $P_n^x+P_{n+1}^x=P_m$
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 : 9999-12-31
Article Type : Makaleler
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