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Publications (6)

math.NT2015

Another generalization of a theorem of Baker and Davenport

Bo He, Ãkos PintÃ©r, Alain Togbe +1

Dujella and PethÅ, 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,…

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.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.NT2022

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.NT2022

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.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…

Publications (6)

Another generalization of a theorem of Baker and Davenport

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

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

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

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

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

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

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

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

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