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The totient function phi(n), also called Euler's totient function, is defined as the number of positive integers <=n that are relatively prime to (i.e., do not contain any ...

If p is a prime number and a is a natural number, then a^p=a (mod p). (1) Furthermore, if pa (p does not divide a), then there exists some smallest exponent d such that ...

The least genus of any Seifert surface for a given knot. The unknot is the only knot with genus 0. Usually, one denotes by g(K) the genus of the knot K. The knot genus has ...

Determinants are mathematical objects that are very useful in the analysis and solution of systems of linear equations. As shown by Cramer's rule, a nonhomogeneous system of ...

Inference of the truth of an unknown result obtained by noting its similarity to a result already known to be true. In the hands of a skilled mathematician, analogy can be a ...

A subset A of a vector space V is said to be convex if lambdax+(1-lambda)y for all vectors x,y in A, and all scalars lambda in [0,1]. Via induction, this can be seen to be ...

Define the Euler measure of a polyhedral set as the Euler integral of its indicator function. It is easy to show by induction that the Euler measure of a closed bounded ...

The n-hypercube graph, also called the n-cube graph and commonly denoted Q_n or 2^n, is the graph whose vertices are the 2^k symbols epsilon_1, ..., epsilon_n where ...

Chess is a two-player board game believed to have been played in India as early as the sixth century AD. In different parts of this world, different chess games are played. ...

Gödel's first incompleteness theorem states that all consistent axiomatic formulations of number theory which include Peano arithmetic include undecidable propositions ...