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A finite group G has a finite number of conjugacy classes and a finite number of distinct irreducible representations. The group character of a group representation is ...

A divisor, also called a factor, of a number n is a number d which divides n (written d|n). For integers, only positive divisors are usually considered, though obviously the ...

The Cartesian graph product G=G_1 square G_2, also called the graph box product and sometimes simply known as "the" graph product (Beineke and Wilson 2004, p. 104) and ...

The Hadwiger-Nelson problem asks for the chromatic number of the plane, i.e., the minimum number of colors needed to color the plane if no two points at unit distance one ...

Let X be an arbitrary topological space. Denote the set closure of a subset A of X by A^- and the complement of A by A^'. Then at most 14 different sets can be derived from A ...

Given the Mertens function defined by M(n)=sum_(k=1)^nmu(k), (1) where mu(n) is the Möbius function, Stieltjes claimed in an 1885 letter to Hermite that M(x)x^(-1/2) stays ...

Let n be a positive number having primitive roots. If g is a primitive root of n, then the numbers 1, g, g^2, ..., g^(phi(n)-1) form a reduced residue system modulo n, where ...

A palindromic prime is a number that is simultaneously palindromic and prime. The first few (base-10) palindromic primes are 2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, ...

A periodic continued fraction is a continued fraction (generally a regular continued fraction) whose terms eventually repeat from some point onwards. The minimal number of ...

A point lattice is a regularly spaced array of points. In the plane, point lattices can be constructed having unit cells in the shape of a square, rectangle, hexagon, etc. ...