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An interval is a connected portion of the real line. If the endpoints a and b are finite and are included, the interval is called closed and is denoted [a,b]. If the ...

If a and b are integers not both equal to 0, then there exist integers u and v such that GCD(a,b)=au+bv, where GCD(a,b) is the greatest common divisor of a and b.

The extended greatest common divisor of two integers m and n can be defined as the greatest common divisor GCD(m,n) of m and n which also satisfies the constraint ...

The Hamming distance between two vertices of a hypercube is the number of coordinates at which the two vertices differ.

An idealized mathematical object having a rigorously straight edge which can be used to draw a line segment. Although geometric constructions are sometimes said to be ...

A solution zeta_k=e^(2piik/d) to the cyclotomic equation x^d=1. The de Moivre numbers give the coordinates in the complex plane of the polygon vertices of a regular polygon ...

An n-dimensional vector, i.e., a vector (x_1, x_2, ..., x_n) with n components. In dimensions n greater than or equal to two, vectors are sometimes considered synonymous with ...

Topology

Let A denote an R-algebra, so that A is a vector space over R and A×A->A (1) (x,y)|->x·y. (2) Then A is said to be alternative if, for all x,y in A, (x·y)·y=x·(y·y) (3) ...

The partial differential equation u_(xxx)-1/8u_x^3+u_x(Ae^u+Be^(-u))=0.