On the Brocard-Ramanujan problem and generalizations

• Autorzy: Andrzej Dąbrowski
• Języki publikacji: EN

Abstrakty

EN

Let $p_i$ denote the ith prime. We conjecture that there are precisely 28 solutions to the equation $n² - 1 = p₁^{α₁} ⋯ p_k^{α_k}$ in positive integers n and α₁,..., $α_k$. This conjecture implies an explicit description of the set of solutions to the Brocard-Ramanujan equation. We also propose another variant of the Brocard-Ramanujan problem: describe the set of solutions in non-negative integers of the equation n! + A = x₁²+x₂²+x₃² (A fixed).

Kategorie tematyczne

• 11D85: Representation problems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2012
• Tom: 126
• Numer: 1
• Strony: 105-110

Daty

wydano

2012

Twórcy

autor

Andrzej Dąbrowski

• Institute of Mathematics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland

Identyfikatory

DOI

10.4064/cm126-1-7