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A pentagonal square triangular number is a number that is simultaneously a pentagonal number P_l, a square number S_m, and a triangular number T_n. This requires a solution ...

A number which can be represented by a finite number of additions, subtractions, multiplications, divisions, and finite square root extractions of integers. Such numbers ...

In his Meditationes algebraicae, Waring (1770, 1782) proposed a generalization of Lagrange's four-square theorem, stating that every rational integer is the sum of a fixed ...

Let G be an undirected graph, and let i denote the cardinal number of the set of externally active edges of a spanning tree T of G, j denote the cardinal number of the set of ...

The Narayan number N(n,k) for n=1, 2, ... and k=1, ..., n gives a solution to several counting problems in combinatorics. For example, N(n,k) gives the number of expressions ...

A self-avoiding walk is a path from one point to another which never intersects itself. Such paths are usually considered to occur on lattices, so that steps are only allowed ...

A slightly archaic term for a computer-generated random number. The prefix pseudo- is used to distinguish this type of number from a "truly" random number generated by a ...

A number n for which a shortest chain exists which is a Brauer chain is called a Brauer number. There are infinitely many non-Brauer numbers.

As shown by Schur (1916), the Schur number S(n) satisfies S(n)<=R(n)-2 for n=1, 2, ..., where R(n) is a Ramsey number.

An element of an extension field of a field F which is not algebraic over F. A transcendental number is a complex number which is transcendental over the field Q of rational ...