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Any symmetric polynomial (respectively, symmetric rational function) can be expressed as a polynomial (respectively, rational function) in the elementary symmetric ...

There are two different statements, each separately known as the greatest common divisor theorem. 1. Given positive integers m and n, it is possible to choose integers x and ...

Given an m×n matrix A, the fundamental theorem of linear algebra is a collection of results relating various properties of the four fundamental matrix subspaces of A. In ...

A type of mathematical result which is considered by most logicians as more natural than the metamathematical incompleteness results first discovered by Gödel. Finite ...

If n=1,2 (mod 4), and the squarefree part of n is divisible by a prime p=3 (mod 4), then no difference set of order n exists. Equivalently, if a projective plane of order n ...

The most general form of this theorem states that in a commutative unit ring R, the height of every proper ideal I generated by n elements is at most n. Equality is attained ...

Euler's 6n+1 theorem states that every prime of the form 6n+1, (i.e., 7, 13, 19, 31, 37, 43, 61, 67, ..., which are also the primes of the form 3n+1; OEIS A002476) can be ...

The theorem, originally conjectured by Berge (1960, 1961), that a graph is perfect iff neither the graph nor its graph complement contains an odd graph cycle of length at ...

The asymptotic form of the n-step Bernoulli distribution with parameters p and q=1-p is given by P_n(k) = (n; k)p^kq^(n-k) (1) ∼ 1/(sqrt(2pinpq))e^(-(k-np)^2/(2npq)) (2) ...

Set theory is the mathematical theory of sets. Set theory is closely associated with the branch of mathematics known as logic. There are a number of different versions of set ...