On the class number of certain imaginary quadratic fields

Abstract

Theorem. Let n > 2 n>2 denote an integer, D D the square-free part of 2 n − 1 2^n-1 and h h the class number of the field Q [ − D ] Q[\sqrt {-D}] . Then except for the case n = 6 n=6 , n − 2 n-2 divides h h .