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A universal cellular automaton is a cellular automaton which, like a Turing machine, exhibits universality. von Neumann proved that an automaton consisting of cells with four ...

Let S be a collection of subsets of a finite set X. A subset Y of X that meets every member of S is called the vertex cover, or hitting set. A vertex cover of a graph G can ...

A regular graph that is not strongly regular is known as a weakly regular graph. There are no weakly regular simple graphs on fewer than six nodes, and the numbers on n=6, 7, ...

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 ...

A (-1,0,1)-matrix is a matrix whose elements consist only of the numbers -1, 0, or 1. The number of distinct (-1,0,1)-n×n matrices (counting row and column permutations, the ...

The smallest positive composite number and the first even perfect square. Four is the smallest even number appearing in a Pythagorean triple: 3, 4, 5. In the numerology of ...

The third prime number, which is also the second Fermat prime, the third Sophie Germain prime, and Fibonacci number F_4. It is an Eisenstein prime, but not a Gaussian prime, ...

The smallest composite squarefree number (2·3), and the third triangular number (3(3+1)/2). It is the also smallest perfect number, since 6=1+2+3. The number 6 arises in ...

The AC method is an algorithm for factoring quadratic polynomials of the form p(x)=Ax^2+Bx+C with integer coefficients. As its name suggests, the crux of the algorithm is to ...

In general, polynomial equations higher than fourth degree are incapable of algebraic solution in terms of a finite number of additions, subtractions, multiplications, ...