scholarly journals Gauss' class number problem for imaginary quadratic fields

1985 ◽  
Vol 13 (1) ◽  
pp. 23-38 ◽  
Author(s):  
Dorian Goldfeld
Keyword(s):  
Class Number ◽  
Quadratic Fields ◽  
Imaginary Quadratic Fields ◽  
Number Problem

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

2009 ◽  
Vol 51 (1) ◽  
pp. 187-191 ◽  
Author(s):  
YASUHIRO KISHI
Keyword(s):  
Class Number ◽  
Diophantine Equations ◽  
Quadratic Field ◽  
Imaginary Quadratic Field ◽  
Quadratic Fields ◽  
Imaginary Quadratic Fields ◽  
Positive Integers

AbstractWe 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.

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