Glasgow Mathematical Journal

Research Article

NOTE ON THE DIVISIBILITY OF THE CLASS NUMBER OF CERTAIN IMAGINARY QUADRATIC FIELDS

YASUHIRO KISHIa1

a1 Department of Mathematics, Fukuoka University of Education, Munakata, Fukuoka 811-4192, Japan e-mail: ykishi@fukuoka-edu.ac.jp

Abstract

We prove that the class number of the imaginary quadratic field $\Q(\sqrt{2^{2k}-3^n})$ is divisible by n for any positive integers k and n with 22k < 3n, by using Y. Bugeaud and T. N. Shorey's result on Diophantine equations.

(Received April 08 2008)

(Revised June 03 2008)

(Accepted July 01 2008)

2000 Mathematics Subject Classification

  • 11R11;
  • 11R29