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There are several related theorems involving Hamiltonian cycles of graphs that are associated with Pósa. Let G be a simple graph with n graph vertices. 1. If, for every k in ...

A power series in a variable z is an infinite sum of the form sum_(i=0)^inftya_iz^i, where a_i are integers, real numbers, complex numbers, or any other quantities of a given ...

The Pratt certificate is a primality certificate based on Fermat's little theorem converse. Prior to the work of Pratt (1975), the Lucas-Lehmer test had been regarded purely ...

A prime partition of a positive integer n>=2 is a set of primes p_i which sum to n. For example, there are three prime partitions of 7 since 7=7=2+5=2+2+3. The number of ...

A prime constellation of four successive primes with minimal distance (p,p+2,p+6,p+8). The term was coined by Paul Stäckel (1892-1919; Tietze 1965, p. 19). The quadruplet (2, ...

Pronic numbers are figurate numbers of the form P_n=2T_n=n(n+1), where T_n is the nth triangular number. The first few are 2, 6, 12, 20, 30, 42, 56, 72, 90, 110, ... (OEIS ...

Propositional calculus is the formal basis of logic dealing with the notion and usage of words such as "NOT," "OR," "AND," and "implies." Many systems of propositional ...

A pyramid is a polyhedron with one face (known as the "base") a polygon and all the other faces triangles meeting at a common polygon vertex (known as the "apex"). A right ...

A Pythagorean triple is a triple of positive integers a, b, and c such that a right triangle exists with legs a,b and hypotenuse c. By the Pythagorean theorem, this is ...

Let B_t={B_t(omega)/omega in Omega}, t>=0, be one-dimensional Brownian motion. Integration with respect to B_t was defined by Itô (1951). A basic result of the theory is that ...