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A piecewise regular function that 1. Has a finite number of finite discontinuities and 2. Has a finite number of extrema can be expanded in a Fourier series which converges ...

Given any real number theta and any positive integer N, there exist integers h and k with 0<k<=N such that |ktheta-h|<1/N. A slightly weaker form of the theorem states that ...

Let D be a set of positive numbers containing 1, then the D-distance graph X(D) on a nonempty subset X of Euclidean space is the graph with vertex set X and edge set ...

A divisor, also called a factor, of a number n is a number d which divides n (written d|n). For integers, only positive divisors are usually considered, though obviously the ...

An even number N for which N=0 (mod 4). The first few positive doubly even numbers are 4, 8, 12, 16, ... (OEIS A008586).

Let A and B be two classes of positive integers. Let A(n) be the number of integers in A which are less than or equal to n, and let B(n) be the number of integers in B which ...

There exists an absolute constant C such that for any positive integer m, the discrepancy of any sequence {alpha_n} satisfies ...

Expanded notation is the term given in elementary mathematics education for the expansion of a positive integer in the form sum_(k)b_k10^k, i.e., as a sum of appropriate ...

Using a set of corners of a solid that lie in a plane to form the polygon vertices of a new polygon is called faceting. Such polygons may outline new faces that join to ...

In a 1631 edition of Academiae Algebrae, J. Faulhaber published the general formula for the power sum of the first n positive integers, sum_(k=1)^(n)k^p = H_(n,-p) (1) = ...