Terms of recurrence sequences in the solution sets of generalized Pell equations

DOI10.1142/S1793042122500816zbMath1501.11045OpenAlexW4214745881WikidataQ114071816 ScholiaQ114071816MaRDI QIDQ5082483

P. Sebestyén, Lajos Hajdu

Publication date: 16 June 2022

Published in: International Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s1793042122500816

zbMATH Keywords

recurrence sequencespolynomial-exponential equationsgeneralized Pell equation

Mathematics Subject Classification ID

Quadratic and bilinear Diophantine equations (11D09) Exponential Diophantine equations (11D61) Fibonacci and Lucas numbers and polynomials and generalizations (11B39)

Related Items (1)

Terms of recurrence sequences in the solution sets of norm form equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• $X$-coordinates of Pell equations as sums of two tribonacci numbers
• Linear combinations of prime powers in \(X\)-coordinates of Pell equations
• An exponential Diophantine equation related to the sum of powers of two consecutive terms of a Lucas sequence and \(x\)-coordinates of Pell equations
• Sums of \(S\)-units in the solution sets of generalized Pell equations
• The \(x\)-coordinates of Pell equations and sums of two Fibonacci numbers. II.
• On \(X\)-coordinates of Pell equations which are repdigits
• On \(Y\)-coordinates of Pell equations which are members of a fixed binary recurrence
• Zeckendorf representations with at most two terms to \(x\)-coordinates of Pell equations
• On the \(x\)-coordinates of Pell equations which are products of two Fibonacci numbers
• On the \(x\)-coordinates of Pell equations which are \(k\)-generalized Fibonacci numbers
• Unit Equations in Diophantine Number Theory
• On Y-coordinates of Pell equations which are base 2 rep-digits
• On $X$-coordinates of Pell equations which are repdigits
• Norm form equations with solutions taking values in a multi-recurrence
• On the $x$--coordinates of Pell equations which are products of two: Lucas numbers, Pell numbers
• On the $x-$coordinates of Pell equations which are sums of two Padovan numbers
• On Pillai’s problem with X-coordinates of Pell equations and powers of 2 II

This page was built for publication: Terms of recurrence sequences in the solution sets of generalized Pell equations