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A quadratic equation is a second-order polynomial equation in a single variable x ax^2+bx+c=0, (1) with a!=0. Because it is a second-order polynomial equation, the ...

Let N steps of equal length be taken along a line. Let p be the probability of taking a step to the right, q the probability of taking a step to the left, n_1 the number of ...

A number is said to be squarefree (or sometimes quadratfrei; Shanks 1993) if its prime decomposition contains no repeated factors. All primes are therefore trivially ...

There are four completely different definitions of the so-called Apollonius circles: 1. The set of all points whose distances from two fixed points are in a constant ratio ...

The Mertens constant B_1, also known as the Hadamard-de la Vallee-Poussin constant, prime reciprocal constant (Bach and Shallit 1996, p. 234), or Kronecker's constant ...

Lovász (1970) conjectured that every connected vertex-transitive graph is traceable (Gould, p. 33). This conjecture was subsequently verified for several special orders and ...

An analog of the polyominoes and polyiamonds in which collections of regular hexagons are arranged with adjacent sides. They are also called hexes, hexas, or polyfrobs ...

There are two kinds of power sums commonly considered. The first is the sum of pth powers of a set of n variables x_k, S_p(x_1,...,x_n)=sum_(k=1)^nx_k^p, (1) and the second ...

The prime zeta function P(s)=sum_(p)1/(p^s), (1) where the sum is taken over primes is a generalization of the Riemann zeta function zeta(s)=sum_(k=1)^infty1/(k^s), (2) where ...

A random matrix is a matrix of given type and size whose entries consist of random numbers from some specified distribution. Random matrix theory is cited as one of the ...