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

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

Let X be a metric space, A be a subset of X, and d a number >=0. The d-dimensional Hausdorff measure of A, H^d(A), is the infimum of positive numbers y such that for every ...

Given a positive integer n, a labeled n-digraph is a digraph whose vertex set is {1,...,n}.

Let q be a positive integer, then Gamma_0(q) is defined as the set of all matrices [a b; c d] in the modular group Gamma Gamma with c=0 (mod q). Gamma_0(q) is a subgroup of ...

There are two equivalent definitions for a nilpotent matrix. 1. A square matrix whose eigenvalues are all 0. 2. A square matrix A such that A^n is the zero matrix 0 for some ...

A positive value of n for which x-phi(x)=n has no solution, where phi(x) is the totient function. The first few are 10, 26, 34, 50, 52, ... (OEIS A005278).

A quantity which is either 0 (zero) or negative, i.e., <=0.

A positive even value of n for which phi(x)=n, where phi(x) is the totient function, has no solution. The first few are 14, 26, 34, 38, 50, ... (OEIS A005277).

A number theoretic function is a function whose domain is the set of positive integers.