We prove that when divisibility is added to a residuated multilattice, this causes the multilattice structure to collapse down to a residuated lattice. This motivates the study of semi-divisibility and regularity on residuated multilattices. The ordinal sum construction is also applied to residuated multilattices as a way to construct new examples of both residuated multilattices and consistent...

Divisibility testing plays an important role in areas like cryptography and a fast hardware has many applications. This paper discusses an algorithm for divisibility testing of Variable Long Precision (VLP) numbers and its implementation on a reconfigurable target. The algorithm exhibits a high degree of parallelism and scalability and hence helps in deciding a suitable cost-performance tradeof...

We apply Vojta’s conjecture to blowups and deduce a number of deep statements regarding (generalized) greatest common divisors on varieties, in particular on projective space and on abelian varieties. Special cases of these statements generalize earlier results and conjectures. We also discuss the relationship between generalized greatest common divisors and the divisibility sequences attached ...

A divisibility test of Arend Heyting, for polynomials over a …eld in an intuitionistic setting, may be thought of as a kind of division algorithm. We show that such a division algorithm holds for divisibility by polynomials of content 1 over any commutative ring in which nilpotent elements are zero. In addition, for an arbitary commutative ring R, we characterize those polynomials g such that t...

Investigation of divisibility properties of natural numbers is one of the most important themes in the theory of numbers. Various tools have been developed over the centuries to discover and study the various patterns in the sequence of natural numbers in the context of divisibility. In the present paper, we study the divisibility of natural numbers using the framework of a growing complex netw...

A sequence of rational integers {An} is said to be a divisibility sequence if Am | An whenever m | n. If the divisibility sequence {An} also satisfies a linear recurrence relation of order k, it is said to be a linear divisibility sequence. The best known example of a linear divisibility sequence of order 2 is the Lucas sequence {un}, one particular instance of which is the famous Fibonacci seq...

In this study, we generalize the comparability conditions, addressed in Comparability of ideals and valuation over rings [2], between certain maximal ideals and fractional ideals of D which also force D to be a quasi-local domain. Also, we introduce the notion of an almost totally ordered group and establish that: “An integral domain D is an AVD if and only if the group of divisibility of D is ...

This study investigates experimentally pricing behavior of sellers in duopoly markets with posted prices and market power. The two treatment variables are given by divisibility of the price space and tie breaking rules. A change in divisibility is modeled by making the sellers’ price space finer or coarser. The second treatment variable deals with the rule under which demanded units are allocat...

In this paper, we give a new method to test the divisibility of any positive integer by another. First, we outline the usual test, in which one proceeds from right to left, i.e. the direction opposite the one taken while carrying out long division. After pointing out some of the problems with this method, we give another method, which forms the core of this paper. This latter method works along...

An elliptic divisibility sequence (EDS) is a sequence of integers (Wn)n≥0 generated by the nonlinear recursion satisfied by the division polyomials of an elliptic curve. We give a formula for the sign of Wn for unbounded nonsingular EDS, a typical case being Sign(Wn) = (−1) ⌊nβ⌋ for an irrational number β ∈ R. As an application, we show that the associated sequence of absolute values (|Wn|) can...