Search Results for ""

An integer d is a fundamental discriminant if it is not equal to 1, not divisible by any square of any odd prime, and satisfies d=1 (mod 4) or d=8,12 (mod 16). The function ...

Let p>3 be a prime number, then 4(x^p-y^p)/(x-y)=R^2(x,y)-(-1)^((p-1)/2)pS^2(x,y), where R(x,y) and S(x,y) are homogeneous polynomials in x and y with integer coefficients. ...

A cycle of a finite group G is a minimal set of elements {A^0,A^1,...,A^n} such that A^0=A^n=I, where I is the identity element. A diagram of a group showing every cycle in ...

The numbers H_n=H_n(0), where H_n(x) is a Hermite polynomial, may be called Hermite numbers. For n=0, 1, ..., the first few are 1, 0, -2, 0, 12, 0, -120, 0, 1680, 0, ... ...

The numbers defined by the recurrence relation K_(n+1)=1+min(2K_(|_n/2_|),3K_(|_n/3_|)), with K_0=1. The first few values for n=0, 1, 2, ... are 1, 3, 3, 4, 7, 7, 7, 9, 9, ...

The study of number fields by embedding them in a local field is called local class field theory. Information about an equation in a local field may give information about ...

An N-cluster is a point lattice configuration in which the distance between every pair of points is an integer, no three points are collinear, and no four points are ...

nu(x) = int_0^infty(x^tdt)/(Gamma(t+1)) (1) nu(x,alpha) = int_0^infty(x^(alpha+t)dt)/(Gamma(alpha+t+1)), (2) where Gamma(z) is the gamma function (Erdélyi et al. 1981, p. ...

A sentential formula that contains at least one free variable (Carnap 1958, p. 24). A sentential variable containing no free variables (i.e., all variables are bound) is ...

A regular ring in the sense of commutative algebra is a commutative unit ring such that all its localizations at prime ideals are regular local rings. In contrast, a von ...