On divisibility of the numbers H_n(1), H_n(2) and H_n(3)
Abstract
We will deal with numbers given by the relation
Hn(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 Hn(l), Hn(2) and Hn(3) are found. For example any positive integer n>1 does not divide Hn(2) and n ≡ 2mod4 is the necessary condition for divisibility Hn(l) and Hn(3) by n>2. In addition certain properties of their divisibility are used for finding primes among these numbers.
Keywords
divisibility; congruence; primality
References
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Department of Mathematics, University of Hradec Králové, Czech Republic Czechia
Department of Mathematics, University of Hradec Králové, Czech Republic Czechia
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