Giuga Numbers and the arithmetic derivative

2011/03/11 by J. M. Grau, José María Grau, Grau, José María +3 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #advanced mathematical theories #math.NT #msc:11A99 #msc:11B99

paper · pdf · doi:10.48550/arxiv.1103.2298

arxiv created 2011/03/11 · arxiv updated 2011/03/14

Abstract

We characterize Giuga Numbers as solutions to the equation n'=an+1, with a ∈ ℕ and n' being the arithmetic derivative. Although this fact does not refute Lava's conjecture, it brings doubts about its veracity.

Cited by

• The p-adic Order of Power Sums, the Erdös-Moser Equation, and Bernoulli Numbers

Related

• Arithmetic derivatives through geometry of numbers
• Transcendental numbers as solutions to arithmetic differential equations
• Arithmetic differential equations on GL_n, III: Galois groups
• Densities, Laplace Transforms and Analytic Number Theory
• Investigations on the properties of the arithmetic derivative