Results 151 to 160 of about 1,570,034 (196)

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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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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DIVISIBILITY PROPERTIES OF HIGHER RANK LATTICES

Transformation Groups, 2016
Let \({\mathbb G}\) be an algebraic group over \({\mathbb Q}\) and let \(S\) be a finite set of primes (containing \(\infty\) if \({\mathbb G}({\mathbb R})\) is not compact) such that \({\mathbb G}\) splits over \({\mathbb Q}_p\) for all \(p\in S\). Let \(\Gamma\) be a cocompact lattice in \(G=\prod_{p\in S}{\mathbb G}({\mathbb Q}_p)\). The paper under
Einsiedler, Manfred, Mozes, Shahar
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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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Groups Without Divisibility Property

2018
We conclude the monograph by showing the existence of finite p-groups without Divisibility Property. This is a recent work of Gonzalez-Sanchez and Jaikin-Zapirain [46]. Uniform pro-p-groups, uniform \(\mathbb {Z}_p\)-Lie algebras, continuous cohomology, and existence of a 41-dimensional \(\mathbb {Q}\)-Lie algebra with one dimensional center and ...
Inder Bir Singh Passi, Mahender Singh, Manoj Kumar Yadav   +2 more
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New Observation on Division Property

Proceedings of the 2nd International Conference on Computer Science and Application Engineering, 2018
Division1 property is a generalized integral property proposed by Todo at Eurocrypt 2015, which has been used in the analysis of various symmetric-key algorithms. At Asiacrypt 2017, Sun et al. proposed automatic tools based on Boolean Satisfiability Problem (SAT) to detect the division property of ARX ciphers.
Yiran Xing, Hailun Yan, Xuejia Lai
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Divisibility Properties for Overcubic Partition Triples

Summary: Let \(\overline{bt}(n)\) counts all of the overlined version of the cubic partition triples of a positive integer \(n\). In this paper, we obtain several infinite families of congruences modulo small powers of 2 for \(\overline{bt}(n)\). For example, we obtain \(\overline{bt}(8n+ 7)\equiv 0 \pmod {32}\) and \(\overline{bt} (8 \cdot 9^{\alpha ...
Shivaprasada Nayaka, S., Dharmendra, B. N., Mahesh Kumar, M. C.   +2 more
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Divisibility properties of binomial coefficients

The Mathematical Gazette, 1974
In a very interesting recent article [1] W. A. Broomhead described an investigation carried out by staff and pupils at Tonbridge School of the patterns which result when the numbers in Pascal’s triangle are reduced modulo m .
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4. Property Division on Divorce

2018
At the end of a marriage or civil partnership, it is necessary to consider the practical and financial arrangements for the parties’ future: how they will share the value of the house(s), the pensions, and the savings and investments; who pays the debts; who gets personal belongings and furniture; and who has what income to live on.
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