Let hn denote the class number of Q(2 cos2π/2n+2) which is a cyclic extension of degree 2n over the rational number field Q. There are no known examples of hn > 1. We prove that a prime number ℓ does not divide hn for all n < 1 if ℓ is less than 109 or ℓ satisfies a congruence relation ℓ ≢ ± 1 (mod 32).
ASJC Scopus subject areas
- Algebra and Number Theory