Linear combinations of prime powers in \(X\)-coordinates of Pell equations

DOI10.1007/s11139-019-00213-5zbMath1485.11027OpenAlexW3009949508MaRDI QIDQ2024952

Florian Luca, Harold Erazo, Carlos Alexis Gómez Ruiz

Publication date: 4 May 2021

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11139-019-00213-5

zbMATH Keywords

Pell equationslower bounds for linear forms in logarithmslinear combinations of prime powers

Mathematics Subject Classification ID

Counting solutions of Diophantine equations (11D45) Fibonacci and Lucas numbers and polynomials and generalizations (11B39) Linear forms in logarithms; Baker's method (11J86)

Related Items (3)

Terms of recurrence sequences in the solution sets of generalized Pell equations ⋮ Sums of \(S\)-units in sum of terms of recurrence sequences ⋮ On the \(X\)-coordinates of Pell equations of the form \(px^2\)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Fibonacci and Lucas numbers of the form \(2^a+3^b+5^c\)
• Linear combinations of prime powers in sums of terms of binary recurrence sequences
• Perfect powers in second order linear recurrences
• $X$-coordinates of Pell equations as sums of two tribonacci numbers
• 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
• Classical and modular approaches to exponential Diophantine equations. I: Fibonacci and Lucas perfect powers
• Distinct digits in basebexpansions of linear recurrence sequences
• An explicit lower bound for a homogeneous rational linear form in the logarithms of algebraic numbers. II
• Linear combinations of prime powers in binary recurrence sequences
• On the representation of an integer in two different bases.
• On the Diophantine equation $ax^{2t}+bx^ty+cy^2=d$ and pure powers in recurrence sequences.
• On $X$-coordinates of Pell equations which are repdigits
• On the $x$-coordinates of Pell equations which are rep-digits
• On the $x$-coordinates of Pell equations which are Fibonacci numbers
• On the $x$-coordinates of Pell equations which are Fibonacci numbers II
• THE EQUATIONS 3x²−2 = y² AND 8x²−7 = z²
• Number Theory

This page was built for publication: Linear combinations of prime powers in \(X\)-coordinates of Pell equations