Zobrazeno 1 - 10
of 114
pro vyhledávání: '"primary 11b83"'
Autor:
Tóth, László
We introduce and study the generalized cyclotomic polynomials $\Phi_{A,S,n}(x)$ associated with a regular system $A$ of divisors and an arbitrary set $S$ of positive integers. We show that all of these polynomials have integer coefficients, they can
Externí odkaz:
http://arxiv.org/abs/2405.01278
Autor:
Yamada, Tomohiro
We give explicit upper bounds for coefficients of polynomials appearing in Gauss-Kra\"{i}tchik formula for cyclotomic polynomials. We use a certain relation between elementary symmetric polynomials and power sums polynomials.
Comment: 10 pages,
Comment: 10 pages,
Externí odkaz:
http://arxiv.org/abs/2402.15747
Autor:
Farhi, Bakir
In this note, basing on a certain functional equation of the dilogarithm function, we establish nontrivial lower bounds for the $p$-adic valuation (where $p$ is a given prime number) of some type of rational numbers involving harmonic numbers. Then w
Externí odkaz:
http://arxiv.org/abs/2212.03727
Autor:
O'Bryant, Kevin
Publikováno v:
Ukrains'kyi Matematychnyi Zhurnal, 76(8), Sept 2024, pp 1192-06
A Sidon set is a set of integers containing no nontrivial solutions to the equation $a+b=c+d$. We improve on the lower bound on the diameter of a Sidon set with $k$ elements: if $k$ is sufficiently large and ${\cal A}$ is a Sidon set with $k$ element
Externí odkaz:
http://arxiv.org/abs/2207.07800
Autor:
Dresden, Gregory
Publikováno v:
INTEGERS vol. 22 (2022), article A105
We start with new convolution formulas for $F_n - n^p$ involving only the binomial coefficients. Then, we use those to find direct formulas for the sums $\sum_{i=1}^n i^p F_{n-i}$ and $\sum_{i=1}^n i^p F_i$, and we show how our formulas connect to wo
Externí odkaz:
http://arxiv.org/abs/2206.00115
Autor:
Varona, Juan Luis
Publikováno v:
Journal of Integer Sequences, Vol. 24 (2021), Article 21.10.5
For fixed positive integers $n$, we study the solution of the equation $n = k + p_k$, where $p_k$ denotes the $k$th prime number, by means of the iterative method \[ k_{j+1} = \pi(n-k_j), \qquad k_0 = \pi(n), \] which converges to the solution of the
Externí odkaz:
http://arxiv.org/abs/2111.14234
Autor:
Afifurrahman, Muhammad, Barra, Aleams
Publikováno v:
J. Algebra Comb. Discrete Struct. Appl. 11 3 (2024), 175-187
Let $p$ be a prime, and $q=p^n$ be a prime power. In his works on Sidon sets over $\mathbb{F}_q\times \mathbb{F}_q$, Cilleruelo conjectured about polynomials that could generate $q$-element Sidon sets over $\mathbb{F}_q\times \mathbb{F}_q$. Here, we
Externí odkaz:
http://arxiv.org/abs/2111.08886
Autor:
Rajab, Raouf
In the present paper, we are interested in classifying of Collatz sequences on based to the different behavior of these sequences when their lengths tend to infinity. A Collatz infinite sequence can be defined as an infinite ordered set of positive i
Externí odkaz:
http://arxiv.org/abs/2106.01324
Autor:
Barry, Paul
In this note, we explore two families of sequences associated to a suitable integer sequence: the gap-sum sequence and the gap-product sequence. These are the sums and the products of consecutive numbers not in the original sequence. We give closed f
Externí odkaz:
http://arxiv.org/abs/2104.05593
Autor:
Monroe, Laura
Stern's diatomic sequence is a well-studied and simply defined sequence with many fascinating characteristics. The binary signed-digit (BSD) representation of integers is used widely in efficient computation, coding theory and other applications. We
Externí odkaz:
http://arxiv.org/abs/2103.05810