Armand Noubissie

activity

20222026

collaborators

9 papers

math.NT2026

Large common values of generalized Ankeny-Brauer-Chowla recurrences

Armand Noubissie, Robert F. Tichy

In this paper we count the number of common values shared by two linear recurrence sequences, whose characteristic polynomials are a generalized Ankeny-Brauer-Chowla polynomial and…

math.NT2025

Quantitative growth of multi-recurrence sequences

Clemens Fuchs, Armand Noubissie

In 1982, Schlickewei and Van der Poorten claimed that any multi-recurrence sequence has, essentially, maximal possible growth rate. Fourty years later, Fuchs and Heintze provided a…

math.NT2025

Decidability of multiplicative matrix equations and related Diophantine problems

Sebastian Heintze, Armand Noubissie, Robert F. Tichy

Some new decidability results for multiplicative matrix equations over algebraic number fields are established. In particular, special instances of the so-called knapsack problem a…

math.NT2025

On the Exponential Diophantine Equation $(a^{n} - 1) (b^{n} - 1) = x^{2}$

Armand Noubissie, Alain Togbe, Zhongfeng Zhang

Let $a$ and $b$ be two distinct fixed positive integers such that $min {a, b} > 1.$ First, we correct an oversight from \cite{X-Z}. Then, we show that the equation in the title wit…

math.NT2025

On some ternary Diophantine equations of Signature $(p, p, k)$

Armand Noubissie, Alain Togbe

In this paper, we summarize the work on ternary Diophantine equation of the form $A x^{n} + B y^{n} = c z^{m}$ , where $m \in {2, 3, n}$ , $n ⩾ 7$ is a prime. Moreover, we completely sol…

math.NT2025

Linear Combinations of Factorial and $S$ -unit in a Ternary recurrence sequence with a double root

Florian Luca, Armand Noubissie

Here, we show that if $u_{n} = n 2^{n} \pm 1$ , then the largest prime factor of $u_{n} \pm m!$ for $n \geq 0, m \geq 2$ tends to infinity with $max {m, n}$ . In particular, the largest $n$ partic…

math.NT2025

Quantitative growth of linear recurrences

Armand Noubissie

Let ${u_{n}}_{n}$ be a non-degenerate linear recurrence sequence of integers with Binet's formula given by $u_{n} = \sum_{i = 1}^{m} P_{i} (n) α_{i}^{n} .$ Assume $max_{i} ∣ α_{i} ∣ > 1$ . In 1…

cs.DM2023

Skolem Meets Bateman-Horn

Florian Luca, James Maynard, Armand Noubissie +2

The Skolem Problem asks to determine whether a given integer linear recurrence sequence has a zero term. This problem arises across a wide range of topics in computer science, incl…

math.NT2022

Higher Reciprocity Laws and Ternary Linear Recurrence Sequences

Pieter Moree, Armand Noubissie

We describe the set of prime numbers splitting completely in the non-abelian splitting field of certain monic irreducible polynomials of degree three. As an application we establis…

Large common values of generalized Ankeny-Brauer-Chowla recurrences

Quantitative growth of multi-recurrence sequences

Decidability of multiplicative matrix equations and related Diophantine problems

On the Exponential Diophantine Equation (an−1)(bn−1)=x2

On some ternary Diophantine equations of Signature (p,p,k)

Linear Combinations of Factorial and S-unit in a Ternary recurrence sequence with a double root

Quantitative growth of linear recurrences

Skolem Meets Bateman-Horn

Higher Reciprocity Laws and Ternary Linear Recurrence Sequences

On the Exponential Diophantine Equation $(a^{n} - 1) (b^{n} - 1) = x^{2}$

On some ternary Diophantine equations of Signature $(p, p, k)$

Linear Combinations of Factorial and $S$ -unit in a Ternary recurrence sequence with a double root