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There are several theorems known as the "sandwich theorem." In calculus, the squeeze theorem is also sometimes known as the sandwich theorem. In graph theory, the sandwich ...

The Stiefel-Whitney number is defined in terms of the Stiefel-Whitney class of a manifold as follows. For any collection of Stiefel-Whitney classes such that their cup ...

Let sigma_0(n) and sigma_1(n) denote the number and sum of the divisors of n, respectively (i.e., the zeroth- and first-order divisor functions). A number n is called sublime ...

A witness is a number which, as a result of its number theoretic properties, guarantees either the compositeness or primality of a number n. Witnesses are most commonly used ...

A Z-number is a real number xi such that 0<=frac[(3/2)^kxi]<1/2 for all k=1, 2, ..., where frac(x) is the fractional part of x. Mahler (1968) showed that there is at most one ...

Place two solid spheres of radius 1/2 inside a hollow sphere of radius 1 so that the two smaller spheres touch each other at the center of the large sphere and are tangent to ...

An n×n Latin square is a Latin rectangle with k=n. Specifically, a Latin square consists of n sets of the numbers 1 to n arranged in such a way that no orthogonal (row or ...

Klee's identity is the binomial sum sum_(k=0)^n(-1)^k(n; k)(n+k; m)=(-1)^n(n; m-n), where (n; k) is a binomial coefficient. For m=0, 1, ... and n=0, 1,..., the following ...

An ellipse is a curve that is the locus of all points in the plane the sum of whose distances r_1 and r_2 from two fixed points F_1 and F_2 (the foci) separated by a distance ...

An Achilles number is a positive integer that is powerful (in the sense that each prime factor occurs with exponent greater than one) but imperfect (in the sense that the ...