In this paper, criteria of divisibility of the class number h + of the real cyclotomic field Q(ζp + ζ −1 p) of a prime conductor p and of a prime degree l by primes q the order modulo l of which is l−1 2 , are given. A corollary of these criteria is the possibility to make a computational proof that a given q does not divide h + for any p (conductor) such… (More)
The aim of this paper is to give new results about factorizations of the Fibonacci numbers F n and the Lucas numbers L n. These numbers are defined by the second order recurrence relation a n+2 = a n+1 + a n with the initial terms F 0 = 0, F 1 = 1 and L 0 = 2, L 1 = 1, respectively. Proofs of theorems are done with the help of connections between… (More)
The aim of this paper is to prove the following Theorem Theorem. Let K be an octic subbeld of the eld Q(p + ?1 p) and let p = n 4 + 16 be prime. Then p divides h K if and only if p divides B j for some j = p?1 8 , 3 p?1 8 , 5 p?1 8 , 7 p?1 8 .