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The probability that a random integer between 1 and x will have its greatest prime factor <=x^alpha approaches a limiting value F(alpha) as x->infty, where F(alpha)=1 for ...

A group having an infinite number of elements. Some infinite groups, such as the integers or rationals, are not continuous groups.

The rook is a chess piece that may move any number of spaces either horizontally or vertically per move. The maximum number of nonattacking rooks that may be placed on an n×n ...

A vertex coloring is an assignment of labels or colors to each vertex of a graph such that no edge connects two identically colored vertices. A vertex coloring that minimize ...

The Higman-Sims graph is the unique strongly regular graph on 100 nodes (Higman and Sims 1968, Brouwer 1983, Brouwer and Haemers 1993). It was also constructed independently ...

A function f is said to be an entire modular form of weight k if it satisfies 1. f is analytic in the upper half-plane H, 2. f((atau+b)/(ctau+d))=(ctau+d)^kf(tau) whenever [a ...

The base-2 transcendental number 0.11011011111011011111..._2 (1) (OEIS A014578), where the nth bit is 1 if n is not divisible by 3 and is the complement of the (n/3)th bit if ...

Let R be a number ring of degree n with 2s imaginary embeddings. Then every ideal class of R contains an ideal J such that ||J||<=(n!)/(n^n)(4/pi)^ssqrt(|disc(R)|), where ...

When the group order h of a finite group is a prime number, there is only one possible group of group order h. Furthermore, the group is cyclic.

In a network with three graph edges at each graph vertex, the number of Hamiltonian cycles through a specified graph edge is 0 or even.