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An encoding is a way of representing a number or expression in terms of another (usually simpler) one. However, multiple expressions can also be encoded as a single ...

Little's law states that, under steady state conditions, the average number of items in a queuing system equals the average rate at which the items arrive multiplied by the ...

A generalization of simple majority voting in which a list of quotas {q_0,...,q_n} specifies, according to the number of votes, how many votes an alternative needs to win ...

The number of ways N(m,n) of finding a subrectangle with an m×n rectangle can be computed by counting the number of ways in which the upper right-hand corner can be selected ...

A formula for the permanent of a matrix perm(a_(ij))=(-1)^nsum_(s subset= {1,...,n})(-1)^(|s|)product_(i=1)^nsum_(j in s)a_(ij), where the sum is over all subsets of ...

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

A Mersenne prime is a Mersenne number, i.e., a number of the form M_n=2^n-1, that is prime. In order for M_n to be prime, n must itself be prime. This is true since for ...

For a real number x in (0,1), let m be the number of terms in the convergent to a regular continued fraction that are required to represent n decimal places of x. Then Lochs' ...

The first Göllnitz-Gordon identity states that the number of partitions of n in which the minimal difference between parts is at least 2, and at least 4 between even parts, ...

The prime counting function is the function pi(x) giving the number of primes less than or equal to a given number x (Shanks 1993, p. 15). For example, there are no primes ...