Year: 2026
Type: preprint
Abstract: In this paper, we study the $p$-adic zeros of the Tribonacci sequence $T_n$, for a prime $p$. In particular, we complete the analysis that was done in a 2024 paper of Yuri Bilu by investigating the case of $p=11$. In addition, we investigate the primes $p$ for which at the first two values $T_n$ and $T_{n-1}$ which are both divisible by $p$, both of these are actually divisible by $p^2$, proving under the assumption of a generalisation of the $abc$ conjecture that there are infinitely many $p$ which are not such.
Source: arXiv (Cornell University)
Authors: Baker, Liam, Luca, Florian, Porrill, Kerry
Institution: Max Planck Institute for Software Systems
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214021957