Giuga Numbers and the arithmetic derivative

TL;DR

This paper characterizes Giuga Numbers through a specific equation involving the arithmetic derivative, providing new insights into their properties and implications for Lava's conjecture.

Contribution

It introduces a novel characterization of Giuga Numbers using the arithmetic derivative equation, offering a new perspective on their structure.

Findings

Giuga Numbers satisfy the equation n' = an + 1 for some a in natural numbers.

This characterization does not disprove Lava's conjecture but raises doubts about its validity.

The work links Giuga Numbers to the properties of the arithmetic derivative.

Abstract

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