On Pillai's problem with the Fibonacci and Pell sequences

DOI10.1007/s40590-018-0223-9zbMath1440.11018OpenAlexW2900684276WikidataQ128882252 ScholiaQ128882252MaRDI QIDQ2010830

Luis Manuel Rivera, Florian Luca, Santos Hernández Hernández

Publication date: 28 November 2019

Published in: Boletín de la Sociedad Matemática Mexicana. Third Series (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/21.11116/0000-0004-ED02-F

zbMATH Keywords

Fibonaccilinear form in logarithmsPell sequencesPillai's type problem

Mathematics Subject Classification ID

Counting solutions of Diophantine equations (11D45) Exponential Diophantine equations (11D61) Fibonacci and Lucas numbers and polynomials and generalizations (11B39) Linear forms in logarithms; Baker's method (11J86)

Related Items (10)

On a variant of Pillai problem: integers as difference between generalized Pell numbers and perfect powers ⋮ On a variant of Pillai's problem involving \(S\)-units and Fibonacci numbers ⋮ Unnamed Item ⋮ On a problem of Pillai with Fibonacci numbers and powers of 3 ⋮ On a variant of Pillai's problem with factorials and \(S\)-units ⋮ On the Diophantine equation 𝑈_{𝑛}-𝑏^{𝑚}=𝑐 ⋮ On the problem of Pillai with k-generalized Fibonacci numbers and powers of 3 ⋮ On Pillai’s problem with X-coordinates of Pell equations and powers of 2 II ⋮ Pillai's problem with k-Fibonacci and Pell numbers ⋮ On the problem of Pillai with Pell numbers, Pell–Lucas numbers and powers of 3

Uses Software

• Mathematica

Cites Work

• Unnamed Item
• Unnamed Item
• On a variant of Pillai's problem. II.
• On a problem of Pillai with \(k\)-generalized Fibonacci numbers and powers of 2
• Linear combinations of factorials and \(S\)-units in a binary recurrence sequence
• On a problem of Pillai with Fibonacci numbers and powers of 2
• Classical and modular approaches to exponential Diophantine equations. I: Fibonacci and Lucas perfect powers
• An explicit lower bound for a homogeneous rational linear form in the logarithms of algebraic numbers. II
• On a variant of Pillai’s problem
• Powers of two as sums of two k-Fibonacci numbers
• ON PILLAI'S PROBLEM WITH TRIBONACCI NUMBERS AND POWERS OF 2
• THE EQUATIONS 3x²−2 = y² AND 8x²−7 = z²

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