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An ordered factorization is a factorization (not necessarily into prime factors) in which a×b is considered distinct from b×a. The following table lists the ordered ...

If there is no integer 0<x<p such that x^2=q (mod p), i.e., if the congruence (35) has no solution, then q is said to be a quadratic nonresidue (mod p). If the congruence ...

A primality test that provides an efficient probabilistic algorithm for determining if a given number is prime. It is based on the properties of strong pseudoprimes. The ...

An algorithm for making tables of primes. Sequentially write down the integers from 2 to the highest number n you wish to include in the table. Cross out all numbers >2 which ...

Ramanujan calculated mu=1.45136380... (Hardy 1999, Le Lionnais 1983, Berndt 1994), while the correct value is mu=1.45136923488... (OEIS A070769; Derbyshire 2004, p. 114). The ...

The word "surface" is an important term in mathematics and is used in many ways. The most common and straightforward use of the word is to denote a two-dimensional ...

The confluent hypergeometric function of the second kind gives the second linearly independent solution to the confluent hypergeometric differential equation. It is also ...

The word "convergent" has a number of different meanings in mathematics. Most commonly, it is an adjective used to describe a convergent sequence or convergent series, where ...

Given a sequence {a_n}_(n=1)^infty, a formal power series f(s) = sum_(n=1)^(infty)(a_n)/(n^s) (1) = a_1+(a_2)/(2^s)+(a_3)/(3^s)+... (2) is called the Dirichlet generating ...

The double factorial of a positive integer n is a generalization of the usual factorial n! defined by n!!={n·(n-2)...5·3·1 n>0 odd; n·(n-2)...6·4·2 n>0 even; 1 n=-1,0. (1) ...