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Let a and b be nonzero integers such that a^mb^n!=1 (except when m=n=0). Also let T(a,b) be the set of primes p for which p|(a^k-b) for some nonnegative integer k. Then ...

A relation < is a strict order on a set S if it is 1. Irreflexive: a<a does not hold for any a in S. 2. Asymmetric: if a<b, then b<a does not hold. 3. Transitive: a<b and b<c ...

A graph is strongly perfect if every induced subgraph H has an independent vertex set meeting all maximal cliques of H (Berge and Duchet 1984, Ravindra 1999). Every strongly ...

The subdiagonal of a square matrix is the set of elements directly under the elements comprising the diagonal. For example, in the following matrix, the diagonal elements are ...

Let U subset= C be an open set and f a real-valued continuous function on U. Suppose that for each closed disk D^_(P,r) subset= U and every real-valued harmonic function h ...

If P(n) is a sentential formula depending on a variable n ranging in a set of real numbers, the sentence P(n) for every sufficiently large n (1) means exists N such that P(n) ...

The superdiagonal of a square matrix is the set of elements directly above the elements comprising the diagonal. For example, in the following matrix, the diagonal elements ...

The word "surface" is an important term in mathematics and is used in many ways. The most common and straightforward use of the word is to denote a two-dimensional ...

A surface with boundary is a topological space obtained by identifying edges and vertices of a set of triangles according to all the requirements of a surface except that ...

A symmetric polynomial on n variables x_1, ..., x_n (also called a totally symmetric polynomial) is a function that is unchanged by any permutation of its variables. In other ...