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Consider the inequality sigma(n)<e^gammanlnlnn for integer n>1, where sigma(n) is the divisor function and gamma is the Euler-Mascheroni constant. This holds for 7, 11, 13, ...

In the classical quasithin case of the quasithin theorem, if a group G does not have a "strongly embedded" subgroup, then G is a group of Lie-type in characteristic 2 of Lie ...

A theorem which effectively describes how lengths, areas, volumes, and generalized n-dimensional volumes (contents) are distorted by differentiable functions. In particular, ...

If there exists a rational integer x such that, when n, p, and q are positive integers, x^n=q (mod p), then q is the n-adic residue of p, i.e., q is an n-adic residue of p ...

A theorem which states that if a Kähler form represents an integral cohomology class on a compact manifold, then it must be a projective Abelian variety.

Every nonplanar graph contains either the utility graph K_(3,3) (i.e., the complete bipartite graph on two sets of three vertices) or the pentatope graph K_5 as a ...

For the rational curve of an unperturbed system with rotation number r/s under a map T (for which every point is a fixed point of T^s), only an even number of fixed points ...

The Kuhn-Tucker theorem is a theorem in nonlinear programming which states that if a regularity condition holds and f and the functions h_j are convex, then a solution ...

A theorem due to Conway et al. (1997) which states that, if a positive definite quadratic form with integer matrix entries represents all natural numbers up to 15, then it ...

Chevalley's theorem, also known as the Chevalley-Waring theorem, states that if f is a polynomial in F[x_1,...,x_n], where F is a finite field of field characteristic p, and ...