On members of Lucas sequences which are products of factorials

DOI10.1007/s00605-020-01455-yzbMath1478.11018arXiv1901.01063OpenAlexW3046527368MaRDI QIDQ2197717

Mark Sias, Florian Luca, Shanta Laishram

Publication date: 1 September 2020

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1901.01063

zbMATH Keywords

primes in arithmetic progressionsPell equationsLucas sequence\(abc\) conjecturefactorialsprimitive divisors

Mathematics Subject Classification ID

Binomial coefficients; factorials; (q)-identities (11B65) Counting solutions of Diophantine equations (11D45) Diophantine equations in many variables (11D72) Fibonacci and Lucas numbers and polynomials and generalizations (11B39)

Related Items (6)

On the solutions of the Diophantine equation \(P_n \pm \frac{a(10^m -1)}{9}=k!\) ⋮ On b -repdigits as product of consecutive of Lucas members ⋮ On members of Lucas sequences which are either products of factorials or product of middle binomial coefficients and Catalan numbers ⋮ On \(Y\)-coordinates of Pell equations which are members of a fixed binary recurrence ⋮ On members of Lucas sequences which are products of Catalan numbers ⋮ \(X\)-coordinates of Pell equations in various sequences

Cites Work

• Unnamed Item
• Explicit bounds for primes in arithmetic progressions
• \(F_1F_2F_3F_4F_5F_6F_8F_{10}F_{12}=11!\)
• Products of factorials in binary recurrence sequences
• Existence of primitive divisors of Lucas and Lehmer numbers
• Fibonacci Numbers with the Lehmer Property
• The large sieve
• Primitive divisors of Lucas and Lehmer sequences, III
• Products of factorials which are powers

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