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Nonstandard analysis is a branch of mathematical logic which introduces hyperreal numbers to allow for the existence of "genuine infinitesimals," which are numbers that are ...

If a is an arbitrary integer relatively prime to n and g is a primitive root of n, then there exists among the numbers 0, 1, 2, ..., phi(n)-1, where phi(n) is the totient ...

A permutation group is a finite group G whose elements are permutations of a given set and whose group operation is composition of permutations in G. Permutation groups have ...

Let n be an integer variable which tends to infinity and let x be a continuous variable tending to some limit. Also, let phi(n) or phi(x) be a positive function and f(n) or ...

The term diamond is another word for a rhombus. The term is also used to denote a square tilted at a 45 degrees angle. The diamond shape is a special case of the superellipse ...

Let (L,<=) be any complete lattice. Suppose f:L->L is monotone increasing (or isotone), i.e., for all x,y in L, x<=y implies f(x)<=f(y). Then the set of all fixed points of f ...

An antimagic square is an n×n array of integers from 1 to n^2 such that each row, column, and main diagonal produces a different sum such that these sums form a sequence of ...

If all the diagonals--including those obtained by "wrapping around" the edges--of a magic square sum to the same magic constant, the square is said to be a panmagic square ...

The word "pole" is used prominently in a number of very different branches of mathematics. Perhaps the most important and widespread usage is to denote a singularity of a ...

The snub cubical graph is the Archimedean graph on 24 nodes and 60 edges obtained by taking the skeleton of the snub cube. It is a quintic graph, is planar, Hamiltonian, and ...