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The Delannoy numbers D(a,b) are the number of lattice paths from (0,0) to (b,a) in which only east (1, 0), north (0, 1), and northeast (1, 1) steps are allowed (i.e., ->, ^, ...

There exist infinitely many odd integers k such that k·2^n-1 is composite for every n>=1. Numbers k with this property are called Riesel numbers, while analogous numbers with ...

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 ...

A generalization of Poncelet's continuity principle made by H. Schubert in 1874-1879. The conservation of number principle asserts that the number of solutions of any ...

A number n is called amenable if it can be built up from integers a_1, a_2, ..., a_k by either addition or multiplication such that sum_(i=1)^na_i=product_(i=1)^na_i=n (1) ...

Let sigma_infty(n) be the sum of the infinitary divisors of a number n. An infinitary perfect number is a number n such that sigma_infty(n)=2n. The first few are 6, 60, 90, ...

The sum of the first n odd numbers is a square number, sum_(k=1)^n(2k-1)=n^2. A sort of converse also exists, namely the difference of the nth and (n-1)st square numbers is ...

An abundant number for which all proper divisors are deficient is called a primitive abundant number (Guy 1994, p. 46). The first few odd primitive abundant numbers are 945, ...

The lower clique number omega_L(G) of a graph G may be defined as the size of a smallest maximal clique in a graph G. It therefore corresponds to the coefficient of the ...

The size of a minimum edge cover in a graph G is known as the edge cover number of G, denoted rho(G). If a graph G has no isolated points, then nu(G)+rho(G)=|G|, where nu(G) ...