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A unit is an element in a ring that has a multiplicative inverse. If a is an algebraic integer which divides every algebraic integer in the field, a is called a unit in that ...

The upper half-plane is the portion of the complex plane {x+iy:x,y in (-infty,infty)} satisfying y=I[z]>0 i.e., {x+iy:x in (-infty,infty),y in (0,infty)}. Common notations ...

Willans' formula is a prime-generating formula due to Willan (1964) that is defined as follows. Let F(j) = |_cos^2[pi((j-1)!+1)/j]_| (1) = {1 for j=1 or j prime; 0 otherwise ...

A variant of the Pollard p-1 method which uses Lucas sequences to achieve rapid factorization if some factor p of N has a decomposition of p+1 in small prime factors.

The quotient W(p)=((p-1)!+1)/p which must be congruent to 0 (mod p) for p to be a Wilson prime. The quotient is an integer only when p=1 (in which case W(1)=2) or p is a ...

The arithmetic mean of a set of values is the quantity commonly called "the" mean or the average. Given a set of samples {x_i}, the arithmetic mean is x^_=1/Nsum_(i=1)^Nx_i. ...

The Burnside problem originated with Burnside (1902), who wrote, "A still undecided point in the theory of discontinuous groups is whether the group order of a group may be ...

The conjugate gradient method is an algorithm for finding the nearest local minimum of a function of n variables which presupposes that the gradient of the function can be ...

The Costa surface is a complete minimal embedded surface of finite topology (i.e., it has no boundary and does not intersect itself). It has genus 1 with three punctures ...

Eigenvalues are a special set of scalars associated with a linear system of equations (i.e., a matrix equation) that are sometimes also known as characteristic roots, ...