Pell and Pell-Lucas numbers as sums of two Jacobsthal numbers

2022/10/08 by Gaber, Ahmed
#11B39 #11D72 #11J70 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2210.04009

Abstract

We solve the two Diophantine equations P_k=J_n+J_m and Q_k=J_n+J_m where \lbrace P_k\rbrace_k≥0, \lbrace Q_k\rbrace_k≥0 and \lbrace J_k\rbrace_k≥0 are the sequences of Pell numbers, Pell-Lucas numbers and Jacobsthal numbers, respectively. The main tool is the theory of linear forms in logarithms.

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