$p$-adic Ducci Sequences: a short note

TL;DR

This paper extends the classical Ducci operator to the p-adic field, exploring its behavior and providing initial results on its properties within this new mathematical context.

Contribution

It formalizes the p-adic Ducci operator and investigates its behavior, offering foundational insights into its properties in the p-adic setting.

Findings

Defined the p-adic Ducci operator $D$

Analyzed the operator's behavior in $\, ext{Q}_p$

Presented initial results as a p-adic counterpart to classical Ducci sequences

Abstract

In this short note we formalized the definition for the Ducci operator $D$ in the context of the $p$-adic field $\mathbb{Q}_p$ as a natural extension of the classical one. Moreover we will describe the behavior of the operator and will provide some simple results as a counterpart to the classical one.