On factorials which are products of factorials

DOI10.1017/S0305004107000308zbMath1132.11017OpenAlexW2043142542MaRDI QIDQ5434682

Florian Luca

Publication date: 7 January 2008

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0305004107000308

zbMATH Keywords

\(ABC\) conjectureDiophantine equation involving factorialsasymptotic density zero

Mathematics Subject Classification ID

Binomial coefficients; factorials; (q)-identities (11B65) Diophantine equations (11D99)

Related Items (9)

On the equation \(n! = a_1! a_2! \cdots a_t!\) ⋮ Variations on the Brocard-Ramanujan equation ⋮ Bounds for the counting function of the Jordan-Pólya numbers ⋮ Power savings for counting solutions to polynomial-factorial equations ⋮ Remark on factorials that are products of factorials ⋮ Squares and factorials in products of factorials ⋮ On the equation \(A!B!=C!\) ⋮ Lower bounds for the greatest prime factor of product of consecutive positive integers ⋮ Finiteness of trivial solutions of factorial products yielding a factorial over number fields

Cites Work

• On the equation \(P(x)=n!\) and a question of Erdős
• The Diophantine Equation n ! + 1 = m²
• On polynomial-factorial diophantine equations

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