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Legendre showed that there is no rational algebraic function which always gives primes. In 1752, Goldbach showed that no polynomial with integer coefficients can give a prime ...

The class of all regular sequences of particularly well-behaved functions equivalent to a given regular sequence. A distribution is sometimes also called a "generalized ...

Let a chess piece make a tour on an n×n chessboard whose squares are numbered from 1 to n^2 along the path of the chess piece. Then the tour is called a magic tour if the ...

Percolation, the fundamental notion at the heart of percolation theory, is a difficult idea to define precisely though it is quite easy to describe qualitatively. From the ...

There are two kinds of power sums commonly considered. The first is the sum of pth powers of a set of n variables x_k, S_p(x_1,...,x_n)=sum_(k=1)^nx_k^p, (1) and the second ...

The (complete) gamma function Gamma(n) is defined to be an extension of the factorial to complex and real number arguments. It is related to the factorial by Gamma(n)=(n-1)!, ...

The number of representations of n by k squares, allowing zeros and distinguishing signs and order, is denoted r_k(n). The special case k=2 corresponding to two squares is ...

There are many formulas of pi of many types. Among others, these include series, products, geometric constructions, limits, special values, and pi iterations. pi is ...

The cubic formula is the closed-form solution for a cubic equation, i.e., the roots of a cubic polynomial. A general cubic equation is of the form z^3+a_2z^2+a_1z+a_0=0 (1) ...

Simply stated, floating-point arithmetic is arithmetic performed on floating-point representations by any number of automated devices. Traditionally, this definition is ...