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arXiv · 2609.22364

On periods of the Tribonacci sequence modulo primes

Liam Baker·Florian Luca·Kerry Porrill
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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.

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Liam Baker, Florian Luca, Kerry Porrill. 2026-09-17. On periods of the Tribonacci sequence modulo primes. https://arxiv.org/abs/2609.22364

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