A. Togbé

activity

20152026

most citedFibonacci and Lucas numbers as products of three repdigits in base

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3 citations · 6 across the 8 of their papers we have counts for

collaborators

9 papers

math.GM2026

There are only finitely many irregular Diophantine quadruples

Bo He, Alain Togbe

A set of $m$ distinct positive integers is called a Diophantine $m$ -tuple if the product of any two distinct elements, increased by one, is a perfect square. A Diophantine quadrupl…

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.NT2022★ 3 cited

Fibonacci and Lucas numbers as products of three repdigits in base $g$

Kouessi Norbert Adedji, Alan Filipin, Alain Togbe

Recall that repdigit in base $g$ is a positive integer that has only one digit in its base $g$ expansion, i.e. a number of the form $a (g^{m} - 1) / (g - 1)$ , for some positive integers $m\…

math.NT2022★ 1 cited

Pell or Pell-Lucas numbers as concatenations of two repdigits in base $b$

Kouessi Norbert Adedji, Alan Filipin, Salah Eddine Rihane +1

Let $b$ be a positive integer such that $2 \leq b \leq 10$ . In this study, we find all Pell or Pell-Lucas numbers as concatenations of two repdigits in base $b$ . As a corollary, it…

math.NT2018

An exponential Diophantine equation related to the difference between powers of two consecutive Balancing numbers

Salah E. Rihane, Bernadette Faye, Florian Luca +1

In this paper, we find all solutions of the exponential Diophantine equation $B_{n + 1}^{x} - B_{n}^{x} = B_{m}$ in positive integer variables $(m, n, x)$ , where $B_{k}$ is the $k$ -th term of the…

math.NT2018

Generalized Cullen Numbers in Linear Recurrence Sequences

Yuri Bilu, Diego Marques, Alain Togb\' e

A Cullen number is a number of the form $m 2^{m} + 1$ , where $m$ is a positive integer. In 2004, Luca and St\u anic\u a proved, among other things, that the largest Fibonacci number in…

math.NT2016★ 2 cited

There is no Diophantine quintuple

Bo He, Alain Togbè, Volker Ziegler

A set of $m$ positive integers ${a_{1}, a_{2}, \dots, a_{m}}$ is called a Diophantine $m$ -tuple if $a_{i} a_{j} + 1$ is a perfect square for all $1 \leq i < j \leq m$ . In 2004 Dujella prove…

math.NT2015

Another generalization of a theorem of Baker and Davenport

Bo He, Ákos Pintér, Alain Togbe +1

Dujella and Pethő, generalizing a result of Baker and Davenport, proved that the set ${1, 3}$ cannot be extended to a Diophantine quintuple. As a consequence of our main result,…