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The Mordell conjecture states that Diophantine equations that give rise to surfaces with two or more holes have only finite many solutions in Gaussian integers with no common ...

The proposal originally made by Georg Cantor that there is no infinite set with a cardinal number between that of the "small" infinite set of integers aleph_0 and the "large" ...

The best known packings of equilateral triangles into an equilateral triangle are illustrated above for the first few cases (Friedman). The best known packings of equilateral ...

This problem is NP-complete (Garey and Johnson 1983).

A problem is NP-hard if an algorithm for solving it can be translated into one for solving any NP-problem (nondeterministic polynomial time) problem. NP-hard therefore means ...

The problem of finding the number of different ways in which a product of n different ordered factors can be calculated by pairs (i.e., the number of binary bracketings of n ...

The Gelfond-Schneider constant is the number 2^(sqrt(2))=2.66514414... (OEIS A007507) that is known to be transcendental by Gelfond's theorem. Both the Gelfand-Schneider ...

Let G=(V,E) be a (not necessarily simple) undirected edge-weighted graph with nonnegative weights. A cut C of G is any nontrivial subset of V, and the weight of the cut is ...

Draw a circle that cuts three given circles perpendicularly. The solution is known as the radical circle of the given three circles. If it lies outside the three circles, ...

A Z-number is a real number xi such that 0<=frac[(3/2)^kxi]<1/2 for all k=1, 2, ..., where frac(x) is the fractional part of x. Mahler (1968) showed that there is at most one ...