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Let s_i be the sum of the products of distinct polynomial roots r_j of the polynomial equation of degree n a_nx^n+a_(n-1)x^(n-1)+...+a_1x+a_0=0, (1) where the roots are taken ...

Voronin (1975) proved the remarkable analytical property of the Riemann zeta function zeta(s) that, roughly speaking, any nonvanishing analytic function can be approximated ...

van der Waerden's theorem is a theorem about the existence of arithmetic progressions in sets. The theorem can be stated in four equivalent forms. 1. If N=C_1 union C_2 union ...

An irrational number is a number that cannot be expressed as a fraction p/q for any integers p and q. Irrational numbers have decimal expansions that neither terminate nor ...

A Pisot number is a positive algebraic integer greater than 1 all of whose conjugate elements have absolute value less than 1. A real quadratic algebraic integer greater than ...

A regular polygon is an n-sided polygon in which the sides are all the same length and are symmetrically placed about a common center (i.e., the polygon is both equiangular ...

The m×n rook graph (confusingly called the m×n grid by Brouwer et al. 1989, p. 440) and also sometimes known as a lattice graph (e.g., Brouwer) is the graph Cartesian product ...

A transcendental number is a (possibly complex) number that is not the root of any integer polynomial, meaning that it is not an algebraic number of any degree. Every real ...

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 ...

A special case of the quadratic Diophantine equation having the form x^2-Dy^2=1, (1) where D>0 is a nonsquare natural number (Dickson 2005). The equation x^2-Dy^2=+/-4 (2) ...