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A doublecross graph is a graph with graph crossing number 2. The numbers of doublecross simple graphs on n=1 nodes are 0, 0, 0, 0, 0, 1, 39, ..., and the numbers of connected ...

Consider a Lucas sequence with P>0 and Q=+/-1. A Fibonacci pseudoprime is a composite number n such that V_n=P (mod n). There exist no even Fibonacci pseudoprimes with ...

A theorem due to Conway et al. (1997) which states that, if a positive definite quadratic form with integer matrix entries represents all natural numbers up to 15, then it ...

Let S(T) be the group of symmetries which map a monohedral tiling T onto itself. The transitivity class of a given tile T is then the collection of all tiles to which T can ...

If f_1(x), ..., f_s(x) are irreducible polynomials with integer coefficients such that no integer n>1 divides f_1(x), ..., f_s(x) for all integers x, then there should exist ...

The maximal number of regions into which space can be divided by n planes is f(n)=1/6(n^3+5n+6) (Yaglom and Yaglom 1987, pp. 102-106). For n=1, 2, ..., these give the values ...

A brute-force method of finding a divisor of an integer n by simply plugging in one or a set of integers and seeing if they divide n. Repeated application of trial division ...

A p-adic integer is a p-adic number of the form sum_(k=m)^(infty)a_kp^k, where m>=0, a_k are integers, and p is prime. It is sufficient to take a_k in the set {0,1,...,p-1}. ...

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

There are a number of attractive polyhedron compounds consisting of five cubes. The first of these (left figures) consists of the arrangement of five cubes in the polyhedron ...