On divisibility of the numbers H_n(1), H_n(2) and H_n(3)

Jaroslav Seibert; Pavel Trojovský

Published: 2003-09-30
Language: EN

Vol. 17 (2003)

On divisibility of the numbers H_n(1), H_n(2) and H_n(3)

Jaroslav Seibert , Pavel Trojovský

Abstract

We will deal with numbers given by the relation
H_n(k) = [(k+1)ⁿ-\binom{n}{2}k²-nk-1]/k³,
where k is equal to 1, 2 or 3. These numbers arise from a generalization Bernoulli's inequality. In this paper some results about divisibility and primality of the numbers H_n(l), H_n(2) and H_n(3) are found. For example any positive integer n>1 does not divide H_n(2) and n ≡ 2mod4 is the necessary condition for divisibility H_n(l) and H_n(3) by n>2. In addition certain properties of their divisibility are used for finding primes among these numbers.

(EN)

Keywords:

divisibility , congruence , primality (EN)

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Citation rules

Seibert, J., & Trojovský, P. (2003). On divisibility of the numbers H_n(1), H_n(2) and H_n(3). Annales Mathematicae Silesianae, 17, 41–51. Retrieved from https://trrest.vot.pl/ojsus/index.php/AMSIL/article/view/14099

Jaroslav Seibert

Affiliation:

Department of Mathematics, University of Hradec Králové, Czech Republic Czechia

Pavel Trojovský

Pavel.Trojovsky@uhk.cz

Affiliation:

Department of Mathematics, University of Hradec Králové, Czech Republic Czechia

Vol. 17 (2003)
Published: 2003-09-30

ISSN: 0860-2107

eISSN: 2391-4238

10.1515/amsil

Publisher

University of Silesia Press

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