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As a consequence of Matiyasevich's refutation of Hilbert's 10th problem, it can be proved that there does not exist a general algorithm for solving a general quartic ...

A generalized hypergeometric function _pF_q(a_1,...,a_p;b_1,...,b_q;x) is a function which can be defined in the form of a hypergeometric series, i.e., a series for which the ...

The word "number" is a general term which refers to a member of a given (possibly ordered) set. The meaning of "number" is often clear from context (i.e., does it refer to a ...

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 ...

An arithmetic progression of primes is a set of primes of the form p_1+kd for fixed p_1 and d and consecutive k, i.e., {p_1,p_1+d,p_1+2d,...}. For example, 199, 409, 619, ...

A graph is said to be regular of degree r if all local degrees are the same number r. A 0-regular graph is an empty graph, a 1-regular graph consists of disconnected edges, ...

Zeros of the Riemann zeta function zeta(s) come in two different types. So-called "trivial zeros" occur at all negative even integers s=-2, -4, -6, ..., and "nontrivial ...

The constant e is base of the natural logarithm. e is sometimes known as Napier's constant, although its symbol (e) honors Euler. e is the unique number with the property ...

The circumcircle is a triangle's circumscribed circle, i.e., the unique circle that passes through each of the triangle's three vertices. The center O of the circumcircle is ...

The cocktail party graph of order n, also called the hyperoctahedral graph (Biggs 1993, p. 17), n-octahedron graph O_n (Jungerman and Ringel 1978), matching graph (Arvind et ...