On the $p$-adic zeros of the Tribonacci sequence

TL;DR

This paper investigates the $p$-adic properties of the Tribonacci sequence, disproving some existing conjectures about its valuations in the $p$-adic number system.

Contribution

It provides new insights into the $p$-adic valuations of Tribonacci numbers and refutes previous conjectures, advancing understanding of their number-theoretic properties.

Findings

Refutes specific conjectures on $p$-adic valuations

Establishes new results on the $p$-adic zeros of Tribonacci numbers

Enhances understanding of the sequence's number-theoretic structure

Abstract

In this paper, we refute some conjectures of Marques and Lengyel concerning the $p$-adic valuations of members of the Tribonacci sequence.