Search Results for ""

The Lucas polynomials are the w-polynomials obtained by setting p(x)=x and q(x)=1 in the Lucas polynomial sequence. It is given explicitly by ...

Every even number is the difference of two consecutive primes in infinitely many ways (Dickson 2005, p. 424). If true, taking the difference 2, this conjecture implies that ...

A binomial number is a number of the form a^n+/-b^n, where a,b, and n are integers. Binomial numbers can be factored algebraically as ...

The following are equivalent definitions for a Galois extension field (also simply known as a Galois extension) K of F. 1. K is the splitting field for a collection of ...

Lehmer's totient problem asks if there exist any composite numbers n such that phi(n)|(n-1), where phi(n) is the totient function? No such numbers are known. However, any ...

A round number is a number that is the product of a considerable number of comparatively small factors (Hardy 1999, p. 48). Round numbers are very rare. As Hardy (1999, p. ...

The Chebotarev density theorem is a complicated theorem in algebraic number theory which yields an asymptotic formula for the density of prime ideals of a number field K that ...

In the algebraic geometry of Grothendieck, a stack refers to a sheaf of categories. In particular, a stack is a presheaf of categories in which the following descent ...

The problem of finding the number of different ways in which a product of n different ordered factors can be calculated by pairs (i.e., the number of binary bracketings of n ...

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 ...