Alain Togbé
Purdue University North Central
Network
Latest external collaboration on country level. Dive into details by clicking on the dots.
Publication
Featured researches published by Alain Togbé.
International Journal of Number Theory | 2008
Florian Luca; Alain Togbé
In this note, we find all the solutions of the Diophantine equation x2 + 2a · 5b = yn in positive integers x, y, a, b, n with x and y coprime and n ≥ 3.
Mathematics of Computation | 2000
Alain Togbé
In this paper, we solve a certain family of diophantine equations associated with a family of cyclic quartic number fields. In fact, we prove that for n < 5 × 10 6 and n ≥ N = 1.191 x 10 19 , with n, n + 2, n 2 + 4 square-free, the Thue equation Φ n (x,y) = x 4 - n 2 x 3 y - (n 3 + 2n 2 + 4n + 2)x 2 y 2 - n 2 xy 3 + y 4 = 1 has no integral solution except the trivial ones: (1, 0), (-1,0), (0,1), (0, -1).
Glasgow Mathematical Journal | 2008
Fadwa S. Abu Muriefah; Florian Luca; Alain Togbé
In this note, we find all the solutions of the Diophantine equation x 2 + 5 a 13 b = y n in positive integers x, y, a, b, n ≥ 3 with x and y coprime.
Periodica Mathematica Hungarica | 2012
Bo He; Alain Togbé
AbstractLet A and k be positive integers. In this paper, we study the Diophantine quadruples
Periodica Mathematica Hungarica | 2009
Bo He; Alain Togbé
Glasgow Mathematical Journal | 2009
Bo He; Alain Togbé
\{ k,A^2 k + 2A,(A + 1)^2 k + 2(A + 1)d\} .
Indagationes Mathematicae | 2008
Bo He; Alain Togbé
International Journal of Number Theory | 2006
Michael A. Bennett; Alain Togbé; P. G. Walsh
If d is a positive integer such that the product of any two distinct elements of the set increased by 1 is a perfect square, then
Integers | 2011
Kevin A. Broughan; Marcos J. González; Ryan H. Lewis; Florian Luca; V. Janitzio Mejía Huguet; Alain Togbé
algorithmic number theory symposium | 2008
Edray Herber Goins; Florian Luca; Alain Togbé
\begin{gathered} d = (4A^4 + 8A^3 + 4A^2 )k^3 + (16A^3 + 24A^2 + 8A)k^2 + \hfill \\ + (20A^2 + 20A + 4)k + (8A + 4) \hfill \\ \end{gathered}