Results 261 to 270 of about 2,992,764 (303)

On the Divisibility Properties of Sequences of Integers

Proceedings of the London Mathematical Society, 1970
Es sei \(a_1 < \ldots\) eine Folge positiver ganzer Zahlen \(A(x) = \sum_{a_1 \leq x}1\). Die Folge \(A_1 < \ldots\) hat die Eigenschaft \(p\) wenn kein \(a\) die Summe zweier größerer \(a\)'s teilt. Die Autoren zeigen, daß jede Folge mit der Eigenschaft \(p\) die Dichte \(0\) hat.
Erdős, Paul, Sárkőzy, András
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On the Division Property of Simon48 and Simon64

2016
Simon is a family of lightweight block ciphers published by the U.S. National Security Agency (NSA) in 2013. Due to its novel and bit-based design, integral cryptanalysis on Simon seems a tough job. At EUROCRYPT 2015 Todo proposed division property which is a generalized integral property, and he applied this technique to searching integral ...
Zejun Xiang 0001, Wentao Zhang, Dongdai Lin   +2 more
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Divisibility Properties of Graded Domains

Canadian Journal of Mathematics, 1982
Let R = ⊕α∊гRα be an integral domain graded by an arbitrary torsionless grading monoid Γ. In this paper we consider to what extent conditions on the homogeneous elements or ideals of R carry over to all elements or ideals of R. For example, in Section 3 we show that if each pair of nonzero homogeneous elements of R has a GCD, then R is a GCD-domain ...
Anderson, D. D., Anderson, David F.
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A division property of the Fibonacci word

Information Processing Letters, 1995
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On divisibility properties of integers of the forma+á

Acta Mathematica Hungarica, 1987
Let \(A\subseteq \{1,2,...,N\}\) be such that \(a+a'\) for \(a\in A\), \(a'\in A\) be all square-free. Then the authors prove the following interesting results. Theorem 1. For \(N>N_0\) there exists an \(A\) such that \(|A| > (1/248)\log N.\) Theorem 2.
Erdős, Paul, Sárközy, A.
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Groups with Divisibility Property-I

2018
Every finite non-cyclic abelian p-group of order greater than \(p^2\) has the property that its order divides that of its group of automorphisms (Theorem 3.34). The problem whether every non-abelian p-group of order greater than \(p^2\) possesses the same property has been a subject of intensive investigation.
Inder Bir Singh Passi, Mahender Singh, Manoj Kumar Yadav   +2 more
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Compact Representation for Division Property

2016
The division property, which is a new method to find integral characteristics, was proposed at Eurocrypt 2015. Thereafter, some applications and improvements have been proposed. The bit-based division property is also one of such improvements, and the accurate integral characteristic of Simon32 is theoretically proved.
Yosuke Todo, Masakatu Morii
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Some Divisibility Properties Concerning Lucas and Elliptic Divisibility Sequences

2022
Consider the following sequences of integers that are respectively called by the Lucas sequences \(\{U_n(P,Q)\}\) and elliptic divisibility sequences \(\{h_n\}\): \[ U_0(P,Q) = 0,\ U_1(P,Q) = 1, \quad U_n(P,Q) = PU_{n-1}(P,Q)-QU_{n-2}(P,Q)\text{ for } n\geq 2 \] and \[ h_{m+n}h_{m-n}=h_{m+1}h_{m-1}h_n^2-h_{n+1}h_{n-1}h_m^2\text{ for all }m\geq n \geq 0.
Panraksa, Chatchawan, Tangboonduangjit, Aram   +1 more
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Separate Property in the Division of Matrimonial Property

The Korean Society Of Family Law, 2022
In the division of matrimonial property at divorce, the properties which were acquired by cooperation of both parties should be divided. Then should separate property be divided, too? Separate property means the property which one party owned before the marriage or inherited or was given from the third party during the marriage. There are many cases in
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On integers with a special divisibility property.

2006
Let \(\lambda \) denote the Carmichael function, i.e.\ for a positive integer \(n\) let \(\lambda (n)\) be the largest order of any element in the multiplicative group \((\mathbb Z/n\mathbb Z)^\times \), and let \(b(n)= \sum _{d| n}\lambda (d)\). The subject of the paper is the set \({\mathcal B}\) of all positive integers \(n\) such that \(b(n)\) is a
Banks, William David, 1964-, Luca, Florian   +1 more
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