Variants of the Diophantine equation

  • Omar Kihel

    Brock University, St. Catharines, Canada
  • Florian Luca

    UNAM, Campus Morelia, Michoacán, Mexico
  • Alain Togbé

    Purdue University North Central, Westville, USA


In this note we study variants of the Brocard–Ramanujan Diophantine equation . For example, Berend and Harmse [1] proved that the equation has only finitely many positive integer solutions when is a fixed integer. Here we find all the integer solutions of this equation when under the additional assumption that is square-free or cube-free, respectively.

Cite this article

Omar Kihel, Florian Luca, Alain Togbé, Variants of the Diophantine equation . Port. Math. 67 (2010), no. 1, pp. 1–11

DOI 10.4171/PM/1855