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The first of the Hardy-Littlewood conjectures. The k-tuple conjecture states that the asymptotic number of prime constellations can be computed explicitly. In particular, ...

An Abelian group is a group for which the elements commute (i.e., AB=BA for all elements A and B). Abelian groups therefore correspond to groups with symmetric multiplication ...

The nth central binomial coefficient is defined as (2n; n) = ((2n)!)/((n!)^2) (1) = (2^n(2n-1)!!)/(n!), (2) where (n; k) is a binomial coefficient, n! is a factorial, and n!! ...

As a part of the study of Waring's problem, it is known that every positive integer is a sum of no more than 9 positive cubes (g(3)=9), that every "sufficiently large" ...

The greatest common divisor, sometimes also called the highest common divisor (Hardy and Wright 1979, p. 20), of two positive integers a and b is the largest divisor common ...

A set of real numbers x_1, ..., x_n is said to possess an integer relation if there exist integers a_i such that a_1x_1+a_2x_2+...+a_nx_n=0, with not all a_i=0. For ...

A matrix is a concise and useful way of uniquely representing and working with linear transformations. In particular, every linear transformation can be represented by a ...

A normal distribution in a variate X with mean mu and variance sigma^2 is a statistic distribution with probability density function ...

A polygon can be defined (as illustrated above) as a geometric object "consisting of a number of points (called vertices) and an equal number of line segments (called sides), ...

The sine function sinx is one of the basic functions encountered in trigonometry (the others being the cosecant, cosine, cotangent, secant, and tangent). Let theta be an ...