Displaying 21 – 40 of 152

Showing per page

Connections between connected topological spaces on the set of positive integers

Paulina Szczuka (2013)

Open Mathematics

In this paper we introduce a connected topology T on the set ℕ of positive integers whose base consists of all arithmetic progressions connected in Golomb’s topology. It turns out that all arithmetic progressions which are connected in the topology T form a basis for Golomb’s topology. Further we examine connectedness of arithmetic progressions in the division topology T′ on ℕ which was defined by Rizza in 1993. Immediate consequences of these studies are results concerning local connectedness of...

Counting monic irreducible polynomials P in 𝔽 q [ X ] for which order of X ( mod P ) is odd

Christian Ballot (2007)

Journal de Théorie des Nombres de Bordeaux

Hasse showed the existence and computed the Dirichlet density of the set of primes p for which the order of 2 ( mod p ) is odd; it is 7 / 24 . Here we mimic successfully Hasse’s method to compute the density δ q of monic irreducibles P in 𝔽 q [ X ] for which the order of X ( mod P ) is odd. But on the way, we are also led to a new and elementary proof of these densities. More observations are made, and averages are considered, in particular, an average of the δ p ’s as p varies through all rational primes.

Gaps between consecutive divisors of factorials

Daniel Berend, J. E. Harmse (1993)

Annales de l'institut Fourier

The set of all divisors of n ! , ordered according to increasing magnitude, is considered, and an upper bound on the gaps between consecutive ones is obtained. We are especially interested in the divisors nearest n ! and obtain a lower bound on their distance.

Gaps between primes in Beatty sequences

Roger C. Baker, Liangyi Zhao (2016)

Acta Arithmetica

We study the gaps between primes in Beatty sequences following the methods in the recent breakthrough by Maynard (2015).

Currently displaying 21 – 40 of 152