Abstract
Here, we find all positive integer solutions of the Diophantine equations in the title, where \((P_n)_{n\ge 0}\) is the Pell sequence \(P_0=0,~P_1=1\) and \(P_{n+2}=2P_{n+1}+P_n\) for all \(n\ge 0\).
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Acknowledgements
We thank the referee for comments which improved the quality of our manuscript. The project started in June 2022, during the CIMPA school at IMSP, Institut de Mathématiques et de Sciences Physiques de l’Université d’Abomey-Calavi. FL and AT thank the institute for the excellent working environment.
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Faye, B., Luca, F., Rihane, S.E. et al. The Diophantine equations \(P_n^x+P_{n+1}^y=P_m^x\) or \(P_n^y+P_{n+1}^x=P_m^x\). Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 117, 89 (2023). https://doi.org/10.1007/s13398-023-01425-7
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DOI: https://doi.org/10.1007/s13398-023-01425-7