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A Thue equation is a Diophantine equation of the form A_nx^n+A_(n-1)x^(n-1)y+A_(n-2)x^(n-2)y^2+...+A_0y^n=M in terms of an irreducible polynomial of degree n>=3 having ...

A unit is an element in a ring that has a multiplicative inverse. If a is an algebraic integer which divides every algebraic integer in the field, a is called a unit in that ...

An equilibrium minimal surface for a crystal or drop which has the least anisotropic surface free energy for a given volume. It is the anisotropic analog of a sphere. In the ...

Zero is the integer denoted 0 that, when used as a counting number, means that no objects are present. It is the only integer (and, in fact, the only real number) that is ...

A graph G having chromatic number chi(G)<=k is called a k-colorable graph (Harary 1994, p. 127). In contrast, a graph having chi(G)=k is said to be a k-chromatic graph. Note ...

Let G be a group, and let S subset= G be a set of group elements such that the identity element I not in S. The Cayley graph associated with (G,S) is then defined as the ...

The regular dodecahedron, often simply called "the" dodecahedron, is the Platonic solid composed of 20 polyhedron vertices, 30 polyhedron edges, and 12 pentagonal faces, ...

The arithmetic mean of a set of values is the quantity commonly called "the" mean or the average. Given a set of samples {x_i}, the arithmetic mean is x^_=1/Nsum_(i=1)^Nx_i. ...

When the elliptic modulus k has a singular value, the complete elliptic integrals may be computed in analytic form in terms of gamma functions. Abel (quoted in Whittaker and ...

An Eulerian graph is a graph containing an Eulerian cycle. The numbers of Eulerian graphs with n=1, 2, ... nodes are 1, 1, 2, 3, 7, 15, 52, 236, ... (OEIS A133736), the first ...