The Diophantine equation Fn = P(x)

DOI10.1142/S1793042120501079zbMath1471.11126OpenAlexW3024626693MaRDI QIDQ4970767

Maciej Ulas, Szabolcs Tengely

Publication date: 7 October 2020

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

Full work available at URL: https://doi.org/10.1142/s1793042120501079

zbMATH Keywords

Fibonacci numbersrecurrence sequencesintegral pointsDiophantine equations

Mathematics Subject Classification ID

Computer solution of Diophantine equations (11Y50) Exponential Diophantine equations (11D61)

Uses Software

• Magma

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Fibonacci numbers at most one away from a perfect power
• Integral points on hyperelliptic curves
• Combinatorial numbers in binary recurrences
• Polynomial values in linear recurrences. II
• The Magma algebra system. I: The user language
• Shifted powers in Lucas-Lehmer sequences
• Classical and modular approaches to exponential Diophantine equations. I: Fibonacci and Lucas perfect powers
• Implementing 2-descent for Jacobians of hyperelliptic curves
• On the Diophantine equation $L_n=\binom{x}{5}$
• Two-cover descent on hyperelliptic curves
• On the height constant for curves of genus two, II
• On the height constant for curves of genus two
• Resultants and discriminants of Chebyshev and related polynomials
• Perfect Pell Powers
• Solving elliptic diophantine equations by estimating linear forms in elliptic logarithms. The case of quartic equations
• Lucas and fibonacci numbers and some diophantine Equations
• On Square Fibonacci Numbers
• Computing integral points on genus 2 curves estimating hyperelliptic logarithms