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

• Published in: Glasgow mathematical journal Vol. 51; no. 1; pp. 187 - 191
• Main Author: KISHI, YASUHIRO
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 01.01.2009
• Subjects: 11R11; 11R29; Mathematics; Quadratic programming; 11R29; 11R11

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.