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Let g 2 and n 1 be integers. In this paper, we shall show that there are infinitely many imaginary quadratic fields whose class number is divisible by 2g and whose discriminant has only two prime divisors. As a corollary, we shall show that there are infinitely many imaginary quadratic fields whose 2-class group is a cyclic group of order divisible by 2n.

Divisibility of class numbers of imaginary quadratic fields whose discriminant has only two prime factors