@article{Emin2025, 
author = {Ahmet Emin},
title = {On the dynamics of the Fermat-like Diophantine equation involving Pell numbers},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {8},
pages = {18524-18540},
keywords = {Pell number, Diophantine equation, linear forms in logarithms, reduction method},
url = {https://www.sciopen.com/article/10.3934/math.2025827},
doi = {10.3934/math.2025827},
abstract = {In this study, we investigated a Fermat-like Diophantine equation involving Pell numbers, specifically examining powers of two that can be represented as the sum of the    x-th powers of any two Pell numbers. To solve the equation              P      m              x              +            P      n              x              =            2      a       for    x  ≥  3, where    m,    n,    x, and    a are non-negative integers, we employed Baker's theory of linear forms in logarithms, a modified version of the Baker-Davenport reduction method, and properties of continued fractions. Our results extend previous findings for    x  =  1 and    x  =  2, shedding light on the interplay between Pell numbers and powers of two in this exponential context.}
}