共查询到20条相似文献,搜索用时 156 毫秒
1.
Let \(B_\ell (n)\) denote the number of \(\ell \)-regular bipartitions of n. In this paper, we prove several infinite families of congruences satisfied by \(B_\ell (n)\) for \(\ell \in {\{5,7,13\}}\). For example, we show that for all \(\alpha >0\) and \(n\ge 0\), and
相似文献
$$\begin{aligned} B_5\left( 4^\alpha n+\frac{5\times 4^\alpha -2}{6}\right)\equiv & {} 0 \ (\text {mod}\ 5),\\ B_7\left( 5^{8\alpha }n+\displaystyle \frac{5^{8\alpha }-1}{2}\right)\equiv & {} 3^\alpha B_7(n)\ (\text {mod}\ 7) \end{aligned}$$
$$\begin{aligned} B_{13}\left( 5^{12\alpha }n+5^{12\alpha }-1\right) \equiv B_{13}(n)\ (\text {mod}\ 13). \end{aligned}$$
2.
Periodica Mathematica Hungarica - For any positive integer m, let $$\mathbb {Z}_{m}$$ be the set of residue classes modulo m. For $$A\subseteq \mathbb {Z}_{m}$$ and $$\overline{n}\in \mathbb... 相似文献
3.
Let \(a_{\ell ,m}(n)\) denote the number of \((\ell ,m)\)-regular partitions of a positive integer n into distinct parts, where \(\ell \) and m are relatively primes. In this paper, we establish several infinite families of congruences modulo 2 for \(a_{3,5}(n)\). For example, where \(\alpha , \beta \ge 0\).
相似文献
$$\begin{aligned} a_{3, 5}\left(2^{6\alpha +4}5^{2\beta }n+\frac{ 2^{6\alpha +3}5^{2\beta +1}-1}{3}\right) \equiv 0 , \end{aligned}$$
4.
Positivity - The result of the title is: an archimedean $$\ell $$ -group with weak unit A is (isomorphic to) $$C(\mathcal {L})$$ for some (identifiable) locale $$\mathcal {L}$$ (or, $$\mathbb... 相似文献
5.
Periodica Mathematica Hungarica - Let $$n\ne 0$$ be an integer. A set of m distinct positive integers $$\{a_1,a_2,\ldots ,a_m\}$$ is called a D(n)-m-tuple if $$a_ia_j + n$$ is a perfect square for... 相似文献
6.
Periodica Mathematica Hungarica - Let N be a positive integer, $${\mathbb {A}}$$ be a nonempty subset of $${\mathbb {Q}}$$ and $$\alpha =\dfrac{\alpha _{1}}{\alpha _{2}}\in {\mathbb {A}}{\setminus... 相似文献
7.
Journal of Algebraic Combinatorics - Let $$\mathcal {A}$$ be a Weyl arrangement in an $$\ell $$ -dimensional Euclidean space. The freeness of restrictions of $$\mathcal {A}$$ was first settled by a... 相似文献
8.
9.
Shin-ichiro Seki 《The Ramanujan Journal》2016,39(1):201-224
For a non-negative integer \(n\), let \(E_n\) be the \(n\) th Euler number. In this note, for any positive integer \(n\), we prove the following congruences: Our proof is based on induction on \(n\) and elementary direct calculations.
相似文献
$$\begin{aligned} {\left\{ \begin{array}{ll} E_{4n} \equiv 380n-375 \pmod {10^3}, \\ E_{4n+2} \equiv -460n+399 \pmod {10^3}. \end{array}\right. } \end{aligned}$$
10.
Central European Journal of Operations Research - In this paper, we give a necessary and sufficient criterion for the existence of the $$\ell _p$$ -norm estimate for the nonlinear $$\ell _p$$ -norm... 相似文献
11.
Cristofari Andrea De Santis Marianna Lucidi Stefano Rinaldi Francesco 《Computational Optimization and Applications》2022,83(2):693-721
Computational Optimization and Applications - The $$\ell _1$$ -ball is a nicely structured feasible set that is widely used in many fields (e.g., machine learning, statistics and signal analysis)... 相似文献
12.
Acta Mathematica Hungarica - Let n be a positive integer. We show that if the equation $$(1) \qquad \qquad \qquad x^4+2^ny^4=z^4$$ has a solution (x,y,z) in a cubic number field K with $$xyz \neq... 相似文献
13.
Periodica Mathematica Hungarica - For a given integer $$k\ge 3$$ , a sequence A of nonnegative integers is called an $$AP_k$$ -covering sequence if there exists an integer $$n_0$$ such... 相似文献
14.
The Ramanujan Journal - The partition function $$ p_{[1^c\ell ^d]}(n)$$ can be defined using the generating function $$\begin{aligned} \sum _{n=0}^{\infty }p_{[1^c{\ell }^d]}(n)q^n=\prod... 相似文献
15.
Periodica Mathematica Hungarica - For the Fibonacci sequence the identity $$F_n^2+F_{n+1}^2 = F_{2n+1}$$ holds for all $$n \ge 0$$ . Let $${\mathcal {X}}:= (X_\ell )_{\ell \ge 1}$$ be the sequence... 相似文献
16.
Mathematische Zeitschrift - In this paper, we introduce a condition ( $$\mathrm {F}_m'$$ ) on a field K, for a positive integer m, that generalizes Serre’s condition (F) and which still... 相似文献
17.
Periodica Mathematica Hungarica - A positive integer n is called an r-full integer if for all primes $$p\mid n$$ we have $$p^r\mid n.$$ Let p be an odd prime. For $$\gcd (n,p)=1$$, the smallest... 相似文献
18.
Designs, Codes and Cryptography - Given an integer $$k\ge 3$$ and a group G of odd order, if there exists a 2-(v, k, 1)-design and if v is sufficiently large then there... 相似文献
19.
Summary.
Let
We say that
preserves the distance d 0 if
for each
implies
Let A
n
denote the set of all positive numbers
d such that any map
that preserves unit distance preserves also distance
d.
Let D
n
denote the set of all positive numbers
d with the property: if
and
then there exists a finite set
S
xy
with
such that any map
that preserves unit distance preserves also the distance between
x and y.
Obviously,
We prove:
(1)
(2)
for n 2
D
n
is a
dense subset of
(2) implies that each mapping
f
from
to
(n 2)
preserving unit distance preserves all distances,
if f is continuous with respect to the product topologies
on
and
相似文献
20.
Archiv der Mathematik - We prove a solvability theorem for the Stieltjes problem on $$\mathbb {R}^d$$ which is based on the multivariate Stieltjes condition $$\sum _{n=1}^\infty... 相似文献