Variants of the Diophantine equation
Omar Kihel
Brock University, St. Catharines, CanadaFlorian Luca
UNAM, Campus Morelia, Michoacán, MexicoAlain Togbé
Purdue University North Central, Westville, USA
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Abstract
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