scispace - formally typeset
Search or ask a question
Topic

Divisor

About: Divisor is a research topic. Over the lifetime, 2462 publications have been published within this topic receiving 21394 citations. The topic is also known as: factor & submultiple.


Papers
More filters
Journal ArticleDOI
TL;DR: In this article, it was shown that the fourth power-free element of the divisibility sequence generated by a non-torsion point on the elliptic curve always has a primitive divisor.
Abstract: Let $P$ be a non-torsion point on the elliptic curve $E_{a}: y^{2}=x^{3}+ax$. We show that if $a$ is fourth-power-free and either $n>2$ is even or $n>1$ is odd with $x(P)<0$ or $x(P)$ a perfect square, then the $n$-th element of the elliptic divisibility sequence generated by $P$ always has a primitive divisor.

9 citations

Journal ArticleDOI
Akinari Hoshi1
TL;DR: In this article, a correspondence between integer solutions to the parametric family of cubic Thue equations X 3 − m X 2 Y − (m + 3 ) X Y 2 − Y 3 = λ where λ > 0 is a divisor of m 2 + 3 m + 9 and isomorphism classes of the simplest cubic fields.

9 citations

Journal ArticleDOI
TL;DR: Droll's result is extended by drawing up a complete list of all graphs having the Ramanujan property for each prime power $p^s$ and arbitrary divisor set ${\cal D}$.
Abstract: A connected $\rho$-regular graph $G$ has largest eigenvalue $\rho$ in modulus. $G$ is called Ramanujan if it has at least $3$ vertices and the second largest modulus of its eigenvalues is at most $2\sqrt{\rho-1}$. In 2010 Droll classified all Ramanujan unitary Cayley graphs. These graphs of type ${\rm ICG}(n,\{1\})$ form a subset of the class of integral circulant graphs ${\rm ICG}(n,{\cal D})$, which can be characterised by their order $n$ and a set $\cal D$ of positive divisors of $n$ in such a way that they have vertex set $\mathbb{Z}/n\mathbb{Z}$ and edge set $\{(a,b):\, a,b\in\mathbb{Z}/n\mathbb{Z} ,\, \gcd(a-b,n)\in {\cal D}\}$. We extend Droll's result by drawing up a complete list of all graphs ${\rm ICG}(p^s,{\cal D})$ having the Ramanujan property for each prime power $p^s$ and arbitrary divisor set ${\cal D}$.

9 citations

Journal ArticleDOI
TL;DR: An infinite class of 3-designs and one 4-design is constructed by means of a generalization of the method of [1], where v − 1 is any odd divisor of ( k 2 ) which is greater than 2k.

9 citations

Patent
Linda Anne Kovacs1
21 Aug 1995
TL;DR: A method for determining a combination of shift operations whose results, when added, or added and subtracted in combination, give any desired accuracy for integer division by a known integer divisor is presented in this article.
Abstract: A method for determining a combination of shift operations whose results, when added, or added and subtracted in combination, give any desired accuracy for integer division by a known integer divisor.

9 citations


Network Information
Related Topics (5)
Conjecture
24.3K papers, 366K citations
93% related
Cohomology
21.5K papers, 389.8K citations
92% related
Holomorphic function
19.6K papers, 287.8K citations
91% related
Algebraic number
20.6K papers, 315.6K citations
90% related
Abelian group
30.1K papers, 409.4K citations
89% related
Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20222
2021157
2020172
2019127
2018120
2017140