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Abstract Algebra

A prime number (or prime integer, often simply called a "prime" for short) is a positive integer p>1 that has no positive integer divisors other than 1 and p itself. More ...

Legendre showed that there is no rational algebraic function which always gives primes. In 1752, Goldbach showed that no polynomial with integer coefficients can give a prime ...

In mathematics, a knot is defined as a closed, non-self-intersecting curve that is embedded in three dimensions and cannot be untangled to produce a simple loop (i.e., the ...

A circle is the set of points in a plane that are equidistant from a given point O. The distance r from the center is called the radius, and the point O is called the center. ...

By the duality principle, for every polyhedron, there exists another polyhedron in which faces and polyhedron vertices occupy complementary locations. This polyhedron is ...

A matchstick graph is a simple graph which has a graph embedding that is planar, for which all distances between vertices have unit distance, and which is non-degenerate (so ...

Pascal's triangle is a number triangle with numbers arranged in staggered rows such that a_(nr)=(n!)/(r!(n-r)!)=(n; r), (1) where (n; r) is a binomial coefficient. The ...

A graph is planar if it can be drawn in a plane without graph edges crossing (i.e., it has graph crossing number 0). The number of planar graphs with n=1, 2, ... nodes are 1, ...

The word polyhedron has slightly different meanings in geometry and algebraic geometry. In geometry, a polyhedron is simply a three-dimensional solid which consists of a ...