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Szemerédi's theorem states that every sequence of integers that has positive upper Banach density contains arbitrarily long arithmetic progressions. A corollary states that, ...

Theodorus's constant sqrt(3) has decimal expansion sqrt(3)=1.732050807... (OEIS A002194). It was computed to 10^(10) decimal digits by E. Weisstein on Jul. 23, 2013. The ...

The Thue-Morse constant, also called the parity constant, is given by the concatenated digits of the Thue-Morse sequence P=0.0110100110010110100101100..._2 (1) (OEIS A010060) ...

A uniquely k-colorable graph G is a chi-colorable graph such that every chi-coloring gives the same partition of G (Chao 2001). Examples of uniquely minimal colorable classes ...

Given a pick-7 lottery with 23 numbers that pays a prize to anyone matching at least 4 of the 7 numbers, there is a set of 253 tickets that guarantees a win. This set ...

Given a "good" graph G (i.e., one for which all intersecting graph edges intersect in a single point and arise from four distinct graph vertices), the crossing number is the ...

The greatest common divisor, sometimes also called the highest common divisor (Hardy and Wright 1979, p. 20), of two positive integers a and b is the largest divisor common ...

Every planar graph (i.e., graph with graph genus 0) has an embedding on a torus. In contrast, toroidal graphs are embeddable on the torus, but not in the plane, i.e., they ...

The divisor function sigma_k(n) for n an integer is defined as the sum of the kth powers of the (positive integer) divisors of n, sigma_k(n)=sum_(d|n)d^k. (1) It is ...

An abundant number, sometimes also called an excessive number, is a positive integer n for which s(n)=sigma(n)-n>n, (1) where sigma(n) is the divisor function and s(n) is the ...