P. Tiebekabe

activity

20222026

most citedOn solutions of the Diophantine equation

L_{n} + L_{m} = 3^{a}

4 citations · 8 across the 15 of their papers we have counts for

collaborators

16 papers

math.NT2026

Carmichael numbers of the form $2^{n} p^{m} + 1$ with odd exponent $m$ : refinements of a theorem of Florian Luca, a general independence lemma, and a computational study

Pagdame Tiebekabe

Florian Luca devoted the last paper of his life to the set $K$ of odd positive integers $k$ such that $2^{n} k + 1$ is a Carmichael number for some positive integer $n$ . He pr…

math.GM2026

The Diophantine equation $p^{x} + 6^{y} = z^{2 n}$ : a complete solution for half of the primes

Pagdame Tiebekabe

Let $p$ be a prime number and let $n \geq 1$ be an integer. We completely solve the exponential Diophantine equation $p^{x} + 6^{y} = z^{2 n}$ in positive integers $x, y, z$ for every prim…

math.NT2026

Powers as Fibonacci Sums

Benjamin Earp-Lynch, Simon Earp-Lynch, Omar Kihel +1

We examine the equation $y^{a} = i = 1 \sum k F_{n_{i}}$ for positive integers $y, a \geq 2$ and $k \geq 3$ . This equation can be expressed as a problem in terms of the Zeckendor…

math.GM2026

Sums of three Fibonacci numbers as concatenations of three repdigits in base $b$

Passimzouwé Dagou, Pagdame Tiebekabe, Kouèssi Norbert Adédji +1

In this paper, we investigate sums of three Fibonacci numbers that can be expressed as concatenations of three repdigits in base $b$ , where $b \geq 2$ is an integer. We prove that fo…

math.GM2025

On Narayana numbers which are products of four $b$ -repdigits with a consequence

Passimzouwé Dagou, Pagdame Tiebekabe, Kokou Tcharie

In this paper, we focus on Narayana numbers which can be written as a products of four repdigits in base $g$ , where $g$ is an integer with $g \geq 2$ . We prove that for $g$ between $…

math.GM2025

Generalized Diophantine Approximation on Higher-Dimensional Varieties

Pagdame Tiebekabe

We establish new uniform height inequalities for rational points on higher-dimensional varieties, extending the classical Roth-Schmidt-Subspace paradigm to the Arakelov-theoretic s…

math.NT2024

On the monogenity of pure number fields: application to the existence of canonical number systems

Hamid Ben Yakkou, Brahim Boudine, Pagdame Tiebekabe

Let $m$ be a rational integer with $m \neq = 0, \pm 1$ , and consider the pure number field $K = Q (n m)$ with $n \geq 3$ . Most papers discussing the monogenity of pure…

math.GM2023

Narayana numbers as product of three repdigits in base $g$

Pagdame Tiebekabe, K. R. Kakanou, H. Ben Yakkou

In this paper, we show that there are only finitely many Narayana's numbers which can be written as product of three repdigits in base $g$ with $g \geq 2$ . Moreover, for $2 \leq g…

math.NT2023

The Diophantine equation $a (\frac{b ^{k} - 1}{b - 1}) = U_{n} - U_{m}$

P. Tiebekabe, I. Diouf, A. Tall +1

Here, we find all positive integer solutions of the Diophantine equation in the title, where $(U_{n})_{n ⩾ 0}$ is the generalized Lucas sequence $\mathcal{U}_0=0, \…

math.NT2023★ 1 cited

Narayana's cows numbers which are concatenations of three repdigits in base $ρ$

Pagdame Tiebekabe, Kouèssi Norbert Adédji, Nadjime Pindra +1

Narayana's sequence is a ternary recurrent sequence defined by the recurrence relation $N_{n} = N_{n - 1} + N_{n - 3}$ with initial terms $N_{0} = 0$ and…

math.NT2022★ 1 cited

On common index divisors and monogenity of of the nonic number field defined by a trinomial $x^{9} + a x + b$

Hamid Ben Yakkou, Pagdame Tiebekabe

Let $K$ be a nonic number field generated by a complex root $þ$ of a monic irreducible trinomial $F (x) = x^{9} + a x + b \in Z [x]$ , where $ab \neq = 0$ . Let $i (K)$ be the index of $K$ . A…

math.NT2022

On the Diophantine equation $k = 1 \sum 5 F_{n_{k}} = 2^{a}$

Pagdame Tiebekabe, Ismaïla Diouf

Let $(F_{n})_{n \geq 0}$ be the Fibonacci sequence given by $F_{0} = 0, F_{1} = 1$ and $F_{n + 2} = F_{n + 1} + F_{n}$ for $n \geq 0$ . In this paper, we have determined all the powers of 2 which…

math.NT2022

On solutions of the Diophantine equation $P_{m} - L_{n} = c$

Pagdame Tiebekabe, Serge Adonsou, Ismaïla Diouf

\noindent In this article, we determine all the integers $c$ having at least two representations as difference between two linear recurrent sequences. This is a variant of the Pill…

math.NT2022★ 2 cited

On Pillai's problem involving two linear recurrent sequences : Padovan and Fibonacci

Pagdame Tiebekabe, Serge Adonsou

In this paper, we find all integers $c$ having at least two representations as a difference between linear recurrent sequences. This problem is a pillai problem involving Padovan a…

math.NT2022★ 4 cited

On solutions of the Diophantine equation $L_{n} + L_{m} = 3^{a}$

Pagdame Tiebekabe, Ismaila Diouf

Let $(L_{n})_{n \geq 0}$ be the Lucas sequence given by $L_{0} = 2, L_{1} = 1$ and $L_{n + 2} = L_{n + 1} + L_{n}$ for $n \geq 0$ . In this paper, we are interested in finding all powers of three…

math.NT2022

On solutions of the Diophantine equation $F_{n_{1}} + F_{n_{2}} + F_{n_{3}} + F_{n_{4}} = 2^{a}$

Pagdame Tiebekabe, Ismaïla Diouf

Let $(F_{n})_{n \geq 0}$ be the Fibonacci sequence given by $F_{0} = 0, F_{1} = 1$ and $F_{n + 2} = F_{n + 1} + F_{n}$ for $n \geq 0$ . In this paper, we solve all powers of two which are sums of…

Carmichael numbers of the form 2npm+1 with odd exponent m: refinements of a theorem of Florian Luca, a general independence lemma, and a computational study

The Diophantine equation px+6y=z2n: a complete solution for half of the primes

Powers as Fibonacci Sums

Sums of three Fibonacci numbers as concatenations of three repdigits in base b

On Narayana numbers which are products of four b-repdigits with a consequence

Generalized Diophantine Approximation on Higher-Dimensional Varieties

On the monogenity of pure number fields: application to the existence of canonical number systems

Narayana numbers as product of three repdigits in base g

The Diophantine equation a(b−1bk−1​)=Un​−Um​

Narayana's cows numbers which are concatenations of three repdigits in base ρ

On common index divisors and monogenity of of the nonic number field defined by a trinomial x9+ax+b

On the Diophantine equation k=1∑5​Fnk​​=2a

On solutions of the Diophantine equation Pm​−Ln​=c

On Pillai's problem involving two linear recurrent sequences : Padovan and Fibonacci

On solutions of the Diophantine equation Ln​+Lm​=3a

On solutions of the Diophantine equation Fn1​​+Fn2​​+Fn3​​+Fn4​​=2a

Carmichael numbers of the form $2^{n} p^{m} + 1$ with odd exponent $m$ : refinements of a theorem of Florian Luca, a general independence lemma, and a computational study

The Diophantine equation $p^{x} + 6^{y} = z^{2 n}$ : a complete solution for half of the primes

Sums of three Fibonacci numbers as concatenations of three repdigits in base $b$

On Narayana numbers which are products of four $b$ -repdigits with a consequence

Narayana numbers as product of three repdigits in base $g$

The Diophantine equation $a (\frac{b ^{k} - 1}{b - 1}) = U_{n} - U_{m}$

Narayana's cows numbers which are concatenations of three repdigits in base $ρ$

On common index divisors and monogenity of of the nonic number field defined by a trinomial $x^{9} + a x + b$

On the Diophantine equation $k = 1 \sum 5 F_{n_{k}} = 2^{a}$

On solutions of the Diophantine equation $P_{m} - L_{n} = c$

On solutions of the Diophantine equation $L_{n} + L_{m} = 3^{a}$

On solutions of the Diophantine equation $F_{n_{1}} + F_{n_{2}} + F_{n_{3}} + F_{n_{4}} = 2^{a}$