A note on the divisibility of class numbers of imaginary quadratic fields Q(root a(2)-k(n))

作者：Ito Akiko^*

来源：Proceedings of the Japan Academy Series A-Mathematical Sciences, 2011, 87(9): 151-155.

DOI：10.3792/pjaa.87.151

• Class numbers
• imaginary quadratic fields
• primitive divisors of Lucas numbers

Let n > 1 be an integer, k > 1 be an odd integer and a > 0 be an even integer. Suppose a(2) + b(2)d = k(n), where d not equal 1,3 is a positive odd square-free integer and gcd(a, bd) = 1. In this paper, we describe imaginary quadratic fields Q(root a(2) - k(n)) explicitly whose class numbers are divisible by n if d 1, 5, 7 mod 8 or d 3 mod 8 with (n, 3) = 1 under certain conditions.

• 出版日期2011-11