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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 ...

z^p-y^p=(z-y)(z-zetay)...(z-zeta^(p-1)y), where zeta=e^(2pii/p) (a de Moivre number) and p is a prime.

If f(z) is regular and of the form O(e^(k|z|)) where k<pi, for R[z]>=0, and if f(z)=0 for z=0, 1, ..., then f(z) is identically zero.

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 ...

The three points determined on three coplanar edges of a tetrahedron by the external bisecting planes of the opposite dihedral angles are collinear. Furthermore, this line ...

The internal (external) bisecting plane of a dihedral angle of a tetrahedron divides the opposite edge in the ratio of the areas of the adjacent faces.

For every positive integer n, there exists a sphere which has exactly n lattice points on its surface. The sphere is given by the equation ...