On recurrences of Fahr and Ringel arising in graph theory.
On recurrent mod p sequences.
On Rédei's theory of the Pell equation.
On reduced Arakelov divisors of real quadratic fields
We generalize the concept of reduced Arakelov divisors and define C-reduced divisors for a given number C ≥ 1. These C-reduced divisors have remarkable properties, similar to the properties of reduced ones. We describe an algorithm to test whether an Arakelov divisor of a real quadratic field F is C-reduced in time polynomial in with the discriminant of F. Moreover, we give an example of a cubic field for which our algorithm does not work.
On regular Frobenius bases.
On Regularities of the Distribution of Special Sequences.
On relations between -density and -density
In this paper it is discus a relation between -density and -density. A generalization of Šalát’s result concerning this relation in the case of asymptotic density is proved.
On relations between units of normal algebraic number fields and their subfields
On relative integral bases for unramified extensions
0. Introduction. Since ℤ is a principal ideal domain, every finitely generated torsion-free ℤ-module has a finite ℤ-basis; in particular, any fractional ideal in a number field has an "integral basis". However, if K is an arbitrary number field the ring of integers, A, of K is a Dedekind domain but not necessarily a principal ideal domain. If L/K is a finite extension of number fields, then the fractional ideals of L are finitely generated and torsion-free (or, equivalently, finitely generated and...
On relative pure cyclic fields with power integral bases
Let be an extension of a number field , where satisfies the monic irreducible polynomial of prime degree belonging to ( is the ring of integers of ). The purpose of this paper is to study the monogenity of over by a simple and practical version of Dedekind’s criterion characterizing the existence of power integral bases over an arbitrary Dedekind ring by using the Gauss valuation and the index ideal. As an illustration, we determine an integral basis of a pure nonic field with a...
On relatively prime sets.
On relatively prime subsets and supersets.
On repdigit polygonal numbers.
On repetitions in frequency blocks of a generalized Fibonacci sequence.
On representation of cyclotomic fields
On representation of r-th powers by subset sums
On representations of a number as a sum of three triangles
On representations of numbers by sums of squares and quadratic fields
On representations of the Weil group with bounded conductor.
On Representing Integers as Products of the p + 1.