X-coordinates of Pell equations as sums of two tribonacci numbers
Periodica Mathematica Hungarica, 2018•Springer
… In this paper, inspired by the main result of [9], we look at Pell equations (1.1) such that \(X_k\)
is a sum of two Tribonacci numbers for at least two values of k. … The main tools used in this
work are lower bounds for linear forms in logarithms á la Baker and a version of the
Baker–Davenport reduction method from Diophantine approximation, in addition to
elementary properties of Tribonacci numbers and solutions to Pell equations. 2 Preliminaries …
is a sum of two Tribonacci numbers for at least two values of k. … The main tools used in this
work are lower bounds for linear forms in logarithms á la Baker and a version of the
Baker–Davenport reduction method from Diophantine approximation, in addition to
elementary properties of Tribonacci numbers and solutions to Pell equations. 2 Preliminaries …
Abstract
In this paper, we find all positive squarefree integers d such that the Pell equation has at least two positive integer solutions (X, Y) and such that both X and are sums of two Tribonacci numbers.
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