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Let be a complex valued multiplicative function. For any , we compute the value of the determinant where denotes the greatest common divisor of and , which appear in increasing order in rows and columns. Precisely we prove that This means that is a multiplicative function of . The algebraic apparatus associated with this result allows us to prove the following two results. The first one is the characterization of real multiplicative functions , with , as minimal values of certain...
The coefficients of the greatest common divisor of two polynomials and (GCD) can be obtained from the Sylvester subresultant matrix transformed to lower triangular form, where and deg(GCD) needs to be computed. Firstly, it is supposed that the coefficients of polynomials are given exactly. Transformations of for an arbitrary allowable are in details described and an algorithm for the calculation of the GCD is formulated. If inexact polynomials are given, then an approximate greatest...
We give the answer to the question in the title by proving that
is the largest Lucas number expressible as a sum of exactly three repdigits. Therefore, there are many Lucas numbers which are sums of three repdigits.
Nous caractérisons, dans cet article, les fonctions multiplicatives presque périodiques au sens de Bésicovith ayant un spectre de Fourier non vide.
We analise periodic functions (mod r), keeping Cauchy multiplication as the basic tool, and pay particular attention to even functions (mod r) having the property f(n) = f((n,r)) for all n. We provide some new aspects into the Hilbert space structure of even functions (mod r) and make use of linera transformations to interpret the known number-theoretic formulae involving solutions of congruences.
In this paper, we apply character sum estimates to study products of factorials modulo .
A power digraph modulo , denoted by , is a directed graph with as the set of vertices and as the edge set, where and are any positive integers. In this paper we find necessary and sufficient conditions on and such that the digraph has at least one isolated fixed point. We also establish necessary and sufficient conditions on and such that the digraph contains exactly two components. The primality of Fermat number is also discussed.
We give Lambek-Carlitz type characterization for completely multiplicative reduced incidence functions in Möbius categories of full binomial type. The -analog of the Lambek-Carlitz type characterization of exponential series is also established.
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