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If p divides the numerator of the Bernoulli number B_(2k) for 0<2k<p-1, then (p,2k) is called an irregular pair. For p<30000, the irregular pairs of various forms are p=16843 ...

A multinomial series is generalization of the binomial series discovered by Johann Bernoulli and Leibniz. The multinomial series arises in a generalization of the binomial ...

A plot in the complex plane of the points B(t)=S(t)+iC(t), (1) where S(t) and C(t) are the Fresnel integrals (von Seggern 2007, p. 210; Gray 1997, p. 65). The Cornu spiral is ...

Consider a broadcast scheme on a connected graph from an originator vertex v in a graph G consisting of a sequence of parallel calls starting from v. In each time step, every ...

Five point geometry is a finite geometry subject to the following three axioms: 1. there exist exactly five points, 2. each two distinct points have exactly one line on both ...

Triangle centers with triangle center functions of the form alpha=a^n are called nth power points. These points lie along the trilinear curve a^n:b^n:c^n that passes through ...

C. Kimberling has extensively tabulated and enumerated the properties of triangle centers (Kimberling 1994, 1998, and online), denoting the nth center in his numbering scheme ...

In discrete percolation theory, site percolation is a percolation model on a regular point lattice L=L^d in d-dimensional Euclidean space which considers the lattice vertices ...

A principle that was first enunciated by Jakob Bernoulli which states that if we are ignorant of the ways an event can occur (and therefore have no reason to believe that one ...

An algorithm which can be used to find integer relations between real numbers x_1, ..., x_n such that a_1x_1+a_2x_2+...+a_nx_n=0, with not all a_i=0. Although the algorithm ...