scientific article; zbMATH DE number 7569240

zbMath1501.11011MaRDI QIDQ5095312

Luis H. Gallardo

Publication date: 8 August 2022

Full work available at URL: http://math.colgate.edu/~integers/w58/w58.pdf

Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.

zbMATH Keywords

perfect numberscyclotomic polynomialsdiophantine equationsindex of odd perfect numbers

Mathematics Subject Classification ID

Arithmetic functions; related numbers; inversion formulas (11A25) Higher degree equations; Fermat's equation (11D41)

Related Items (1)

A note on the Diophantine equations \(2 l n^2 = 1 + q + \cdots + q^\alpha\) and application to odd perfect numbers

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the radical of a perfect number
• On a remark of Makowski about perfect numbers
• The Nagell-Ljunggren equation \(\frac{x^n-1}{x-1}=y^q\)
• On the Diophantine equation \(\frac{x^3-1}{x-1}=\frac{y^n-1}{y-1}\)
• On the Diophantine equation \(\frac{x^m-1}{x-1}=\frac{y^n-1}{y-1}\).
• A note on the Goormaghtigh equation
• New congruences for odd perfect numbers
• Radical of perfect numbers and perfect numbers among polynomial values
• On the index of an odd perfect number
• On the Nagell-Ljunggren equation $(x^n - 1)/(x - 1) = y^q$
• The third largest prime divisor of an odd perfect number exceeds one hundred
• Goormaghtigh's equation: small parameters
• On the non-existence of odd perfect numbers of form 𝑝^{𝛼}𝑞₁²𝑞₂²⋯𝑞_{𝑡-1}²𝑞_{𝑡}⁴

This page was built for publication: