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The sporadic groups are the 26 finite simple groups that do not fit into any of the four infinite families of finite simple groups (i.e., the cyclic groups of prime order, ...

A statistical test in which assumptions are made about the underlying distribution of observed data.

Lovász (1970) conjectured that every connected vertex-transitive graph is traceable (Gould, p. 33). This conjecture was subsequently verified for several special orders and ...

Thurston's conjecture proposed a complete characterization of geometric structures on three-dimensional manifolds. Before stating Thurston's geometrization conjecture in ...

There are many unsolved problems in mathematics. Some prominent outstanding unsolved problems (as well as some which are not necessarily so well known) include 1. The ...

The Dedekind psi-function is defined by the divisor product psi(n)=nproduct_(p|n)(1+1/p), (1) where the product is over the distinct prime factors of n, with the special case ...

The residue classes of a function f(x) mod n are all possible values of the residue f(x) (mod n). For example, the residue classes of x^2 (mod 6) are {0,1,3,4}, since 0^2=0 ...

Given the sum-of-factorials function Sigma(n)=sum_(k=1)^nk!, SW(p) is the smallest integer for p prime such that Sigma[SW(p)] is divisible by p. If pSigma(n) for all n<p, ...

A witness is a number which, as a result of its number theoretic properties, guarantees either the compositeness or primality of a number n. Witnesses are most commonly used ...

The Paley graph of order q with q a prime power is a graph on q nodes with two nodes adjacent if their difference is a square in the finite field GF(q). This graph is ...