Czechoslovak Mathematical Journal, first online, pp. 1-9


Pell and Pell-Lucas numbers of the form $-2^a-3^b+5^c$

Yunyun Qu, Jiwen Zeng

Received June 1, 2018.   Published online December 2, 2019.

Abstract:  In this paper, we find all Pell and Pell-Lucas numbers written in the form $-2^a-3^b+5^c$, in nonnegative integers $a$, $b$, $c$, with $0\leq\max\{a,b\}\leq c$.
Keywords:  Pell number; Pell-Lucas number; linear form in logarithms; continued fraction; reduction method
Classification MSC:  11B39, 11J86, 11D61
DOI:  10.21136/CMJ.2019.0265-18

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Affiliations:   Yunyun Qu (corresponding author), School of Mathematical Sciences, Xiamen University, No. 422, Siming South Road, Xiamen 361005, Fujian, P. R. China and School of Mathematical Sciences, Guizhou Normal University, No. 116, Baoshan North Road, Guiyang 550001, Guizhou, P. R. China, e-mail: qucloud@163.com; Jiwen Zeng, School of Mathematical Sciences, Xiamen University, No. 422, Siming South Road, Xiamen 361005, Fujian, P. R. China, e-mail: jwzeng@xmu.edu.cn


 
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