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A pair of positive integers (a_1,a_2) such that the equations a_1+a_2x=sigma(a_1)=sigma(a_2)(x+1) (1) have a positive integer solution x, where sigma(n) is the divisor ...

On a computer screen, the pixels indicating a slanted line are selected with Bresenham's algorithm, developed in 1962 while at IBM.

One name for the figure used by Euclid to prove the Pythagorean theorem. It is sometimes also known as the "windmill."

A numerical knot invariant. For a tame knot K, the bridge index is the least bridge number of all planar representations of the knot. The bridge index of the unknot is ...

If the total group of the canonical series is divided into two parts, the difference between the number of points in each part and the double of the dimension of the complete ...

Brocard geometry is that part of triangle geometry concerned with the Brocard points, Brocard triangles, etc.

Brocard's conjecture states that pi(p_(n+1)^2)-pi(p_n^2)>=4 for n>=2, where pi(n) is the prime counting function and p_n is the nth prime. For n=1, 2, ..., the first few ...

The Bron-Kerbosch algorithm is an efficient method for finding all maximal cliques in a graph.

The chromatic number of a graph is at most the maximum vertex degree Delta, unless the graph is complete or an odd cycle, in which case Delta+1 colors are required.

For every positive integer n, there exists a square in the plane with exactly n lattice points in its interior. This was extended by Schinzel and Kulikowski to all plane ...