Density inequalities for a restricted sum of sets of lattice points
Density of M-sets in arithmetic progression
Density of solutions to quadratic congruences
A classical result in number theory is Dirichlet’s theorem on the density of primes in an arithmetic progression. We prove a similar result for numbers with exactly prime factors for . Building upon a proof by E. M. Wright in 1954, we compute the natural density of such numbers where each prime satisfies a congruence condition. As an application, we obtain the density of squarefree with prime factors such that a fixed quadratic equation has exactly solutions modulo .
Der numerische Wert gewisser Reihen.
Der Staudt-Clausen'sche Satz.
Derivative polynomials, Euler polynomials, and associated integer sequences.
Derived sequences.
Dérivées successives d'une puissance entière d'une fonction d'une variable, dérivées successives d'une fonction de fonction et application à la détermination des nombres de Bernoulli
Deriving divisibility theorems with Burnside's theorem.
Des conditions pour que l'échelle d'une suite récurrente soit irréductible
Des conditions pour que l'échelle d'une suite récurrente soit irréductible
Des mots en arithmétique
Determinant expressions for -harmonic congruences and degenerate Bernoulli numbers.
Determinant Representations of Sequences: A Survey
This is a survey of recent results concerning (integer) matrices whose leading principal minors are well-known sequences such as Fibonacci, Lucas, Jacobsthal and Pell (sub)sequences. There are different ways for constructing such matrices. Some of these matrices are constructed by homogeneous or nonhomogeneous recurrence relations, and others are constructed by convolution of two sequences. In this article, we will illustrate the idea of these methods by constructing some integer matrices of this...
Determinants and inverses of circulant matrices with complex Fibonacci numbers
Let ℱn = circ (︀F*1 , F*2, . . . , F*n︀ be the n×n circulant matrix associated with complex Fibonacci numbers F*1, F*2, . . . , F*n. In the present paper we calculate the determinant of ℱn in terms of complex Fibonacci numbers. Furthermore, we show that ℱn is invertible and obtain the entries of the inverse of ℱn in terms of complex Fibonacci numbers.
Determinants of knots and Diophantine equations
Deux propriétés combinatoires du langage de Lukasiewicz
Deux propriétés décidables des suites récurrentes linéaires
Diagonal checker-jumping and Eulerian numbers for color-signed permutations.
Diagonalization and rationalization of algebraic Laurent series
We prove a quantitative version of a result of Furstenberg [20] and Deligne [14] stating that the diagonal of a multivariate algebraic power series with coefficients in a field of positive characteristic is algebraic. As a consequence, we obtain that for every prime the reduction modulo of the diagonal of a multivariate algebraic power series with integer coefficients is an algebraic power series of degree at most and height at most , where is an effective constant that only depends on...