IJPAM: Volume 16, No. 4 (2004)

ON FEW DIOPHANTINE EQUATIONS RELATED
TO THE BROCARD-RAMANUJAN
DIOPHANTINE EQUATION

Omar Kihel$^1$, Kenneth K. Nwabueze$^2$
$^1$Department of Mathematics
Brock University
St. Catharines, Ontario, L2S 3A1, CANADA
e-mail: okihel@brocku.ca
$^2$Department of Mathematics
University Brunei Darussalam
Gadong, BE 1410, BRUNEI
e-mail: nwabueze@fos.ubd.edu.bn


Abstract.Starting with the Diophantine equation $P(n)n! +x^{q}= y^{q}, $ an inequality relating $n,$ $y$, and $q$ is exhibited. Moreover, some calculations of a variation of the Brocard-Ramanujan Diophantine equation is reported.

Received: July 11, 2004

AMS Subject Classification: 11D85, 11Y50

Key Words and Phrases: Brocard-Ramanujan, Diophantine equation, quadratic reciprocity, linear forms in logarithms

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2004
Volume: 16
Issue: 4