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NOTE ON THE DIVISIBILITY OF THE CLASS NUMBER OF CERTAIN IMAGINARY QUADRATIC FIELDS
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 2 2 k < 3 n , by using Y. Bugeaud and T. N. Shorey's result on Diophantine equations.