On generalized Mersenne Primes and class-numbers of equivalent quadratic fields and cyclotomic fields

In this paper we define equivalent quadratic fields and prove that generalized Mersenne primes generate a family of infinitely many equivalent quadratic fields with equivalent index 2 and whose class numbers are divisible by 3. We also prove that the class-number of the cyclotomic field Q(ζm) , where m∈ N and ζm is a primitive m-th root of unity, is divisible by a certain integer g. © 2014, Sociedad Española de Matemática Aplicada.