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On July 10, 2003, Eric Weisstein computed the numbers of n×n (0,1)-matrices all of whose eigenvalues are real and positive, obtaining counts for n=1, 2, ... of 1, 3, 25, 543, ...

Any nonzero rational number x can be represented by x=(p^ar)/s, (1) where p is a prime number, r and s are integers not divisible by p, and a is a unique integer. The p-adic ...

A Heronian tetrahedron, also called a perfect tetrahedron, is a (not necessarily regular) tetrahedron whose sides, face areas, and volume are all rational numbers. It ...

The process of finding a reduced set of basis vectors for a given lattice having certain special properties. Lattice reduction algorithms are used in a number of modern ...

The Somos sequences are a set of related symmetrical recurrence relations which, surprisingly, always give integers. The Somos sequence of order k, or Somos-k sequence, is ...

The first practical algorithm for determining if there exist integers a_i for given real numbers x_i such that a_1x_1+a_2x_2+...+a_nx_n=0, or else establish bounds within ...

An algorithm used to recursively construct a set of objects from the smallest possible constituent parts. Given a set of k integers (a_1, a_2, ..., a_k) with a_1<a_2<...<a_k, ...

Given two randomly chosen n×n integer matrices, what is the probability D(n) that the corresponding determinants are relatively prime? Hafner et al. (1993) showed that ...

Hoggatt and Denman (1961) showed that any obtuse triangle can be divided into eight acute isosceles triangles. There are 1, 4, 23, 180, 1806, 20198, ... (OEIS A056814) ...

Pre-Algebra