Search Results for ""

The set theory symbol aleph_0 refers to a set having the same cardinal number as the "small" infinite set of integers. The symbol aleph_0 is often pronounced "aleph-null" ...

A d-repdigit is a number composed of repetition of a single digit (in a given base, generally taken as base 10 unless otherwise specified). For example, the beast number 666 ...

Given a number field K, a Galois extension field L, and prime ideals p of K and P of L unramified over p, there exists a unique element sigma=((L/K),P) of the Galois group ...

Let O be an order of an imaginary quadratic field. The class equation of O is the equation H_O=0, where H_O is the extension field minimal polynomial of j(O) over Q, with ...

Given a number field K, there exists a unique maximal unramified Abelian extension L of K which contains all other unramified Abelian extensions of K. This finite field ...

There are at least two theorems known as Weierstrass's theorem. The first states that the only hypercomplex number systems with commutative multiplication and addition are ...

Euclid's second theorem states that the number of primes is infinite. The proof of this can be accomplished using the numbers E_n = 1+product_(i=1)^(n)p_i (1) = 1+p_n#, (2) ...

The Lucas-Lehmer test is an efficient deterministic primality test for determining if a Mersenne number M_n is prime. Since it is known that Mersenne numbers can only be ...

A magic square is a square array of numbers consisting of the distinct positive integers 1, 2, ..., n^2 arranged such that the sum of the n numbers in any horizontal, ...

The quantity twelve (12) is sometimes known as a dozen. It is in turn one twelfth of a gross. Base-12 is known as duodecimal. The Schoolhouse Rock segment "Little Twelvetoes" ...