Sums of factorials in binary recurrence sequences

DOI10.1006/jnth.2001.2718zbMath0995.11008OpenAlexW2080889471MaRDI QIDQ1604981

Florian Luca, George Grossman

Publication date: 10 July 2002

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

Full work available at URL: https://semanticscholar.org/paper/f3b9fb3f2aa79b630712658119dbd0e8c2ec3b7b

zbMATH Keywords

linear forms in logarithms of algebraic numberslargest Fibonacci and Lucas numbersnondegenerate binary linear recurrencesums or differences of two factorials

Mathematics Subject Classification ID

Recurrences (11B37) Fibonacci and Lucas numbers and polynomials and generalizations (11B39) Linear forms in logarithms; Baker's method (11J86) Diophantine equations (11D99)

Related Items (8)

Exponential Diophantine Equations ⋮ Unnamed Item ⋮ On the solutions of the Diophantine equation \(F_n \pm \frac{a (10^m - 1)}{9} = k!\) ⋮ Additive Diophantine equations with binary recurrences, \(\mathcal{S}\)-units and several factorials ⋮ Linear combinations of factorials and \(S\)-units in a binary recurrence sequence ⋮ On factorials expressible as sums of at most three Fibonacci numbers ⋮ Arithmetic properties of the sequence of derangements ⋮ On a Diophantine equation involving Fibonacci numbers and the Ramanujan \(\tau\)-function of factorials

Cites Work

• Effective lower bound for the \(p\)-adic distance between powers of algebraic numbers
• Products of factorials in binary recurrence sequences
• Logarithmic forms and group varieties.
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