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If there exists a rational integer x such that, when n, p, and q are positive integers, x^n=q (mod p), then q is the n-adic residue of p, i.e., q is an n-adic residue of p ...

A vector space V is a set that is closed under finite vector addition and scalar multiplication. The basic example is n-dimensional Euclidean space R^n, where every element ...

A field K is said to be an extension field (or field extension, or extension), denoted K/F, of a field F if F is a subfield of K. For example, the complex numbers are an ...

Two lattice points (x,y) and (x^',y^') are mutually visible if the line segment joining them contains no further lattice points. This corresponds to the requirement that ...

The angles mpi/n (with m,n integers) for which the trigonometric functions may be expressed in terms of finite root extraction of real numbers are limited to values of m ...

The Smarandache function mu(n) is the function first considered by Lucas (1883), Neuberg (1887), and Kempner (1918) and subsequently rediscovered by Smarandache (1980) that ...

A trinomial coefficient is a coefficient of the trinomial triangle. Following the notation of Andrews (1990), the trinomial coefficient (n; k)_2, with n>=0 and -n<=k<=n, is ...

The second knot polynomial discovered. Unlike the first-discovered Alexander polynomial, the Jones polynomial can sometimes distinguish handedness (as can its more powerful ...

A circulant graph is a graph of n graph vertices in which the ith graph vertex is adjacent to the (i+j)th and (i-j)th graph vertices for each j in a list l. The circulant ...

A special case of the Artin L-function for the polynomial x^2+1. It is given by L(s)=product_(p odd prime)1/(1-chi^-(p)p^(-s)), (1) where chi^-(p) = {1 for p=1 (mod 4); -1 ...