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An unsolved problem in mathematics attributed to Lehmer (1933) that concerns the minimum Mahler measure M_1(P) for a univariate polynomial P(x) that is not a product of ...

A statement which appears self-contradictory or contrary to expectations, also known as an antinomy. Curry (1977, p. 5) uses the term pseudoparadox to describe an apparent ...

In the field of percolation theory, the term percolation threshold is used to denote the probability which "marks the arrival" (Grimmett 1999) of an infinite connected ...

A rational number is a number that can be expressed as a fraction p/q where p and q are integers and q!=0. A rational number p/q is said to have numerator p and denominator ...

Let a number n be written in binary as n=(epsilon_kepsilon_(k-1)...epsilon_1epsilon_0)_2, (1) and define b_n=sum_(i=0)^(k-1)epsilon_iepsilon_(i+1) (2) as the number of digits ...

A series-reduced tree is a tree in which all nodes have degree other than 2 (in other words, no node merely allows a single edge to "pass through"). Series-reduced trees are ...

An integer is k-smooth if it has no prime factors >k. The following table gives the first few k-smooth numbers for small k. Berndt (1994, p. 52) called the 7-smooth numbers ...

Stirling's approximation gives an approximate value for the factorial function n! or the gamma function Gamma(n) for n>>1. The approximation can most simply be derived for n ...

Let L be a nontrivial bounded lattice (or a nontrivial complemented lattice, etc.). If every nonconstant lattice homomorphism defined on L is 0,1-separating, then L is a ...

The number one (1), also called "unity," is the first positive integer. It is an odd number. Although the number 1 used to be considered a prime number, it requires special ...