Stanislav Jakubec

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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 that(More)
In the present paper a necessary condition for a cyclic extension of the rationals of prime degree / to have an integral normal basis generated by a unit is given. For a fixed /, this condition implies that there exists at most a finite number of such fields. A computational method for verifying the existence of an integral normal basis generated by a unit(More)
Let K/Q be a cyclic tamely ramified extension of degree 6, then any ambiguous ideal of K has a normal basis. c ©2008 Mathematical Institute Slovak Academy of Sciences In the present paper we will prove that any ambiguous ideal of cyclic algebraic field with squarefree conductor m of degree 6 over the rationals Q has a normal basis. First we recall some(More)
The aim of this paper is to give new results about factorizations of the Fibonacci numbers Fn and the Lucas numbers Ln. These numbers are defined by the second order recurrence relation an+2 = an+1+an with the initial terms F0 = 0, F1 = 1 and L0 = 2, L1 = 1, respectively. Proofs of theorems are done with the help of connections between determinants of(More)
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