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A variant of the Pollard p-1 method which uses Lucas sequences to achieve rapid factorization if some factor p of N has a decomposition of p+1 in small prime factors.

A Dedekind ring is a commutative ring in which the following hold. 1. It is a Noetherian ring and a integral domain. 2. It is the set of algebraic integers in its field of ...

The first of the Hardy-Littlewood conjectures. The k-tuple conjecture states that the asymptotic number of prime constellations can be computed explicitly. In particular, ...

A generalized hypergeometric function _pF_q[alpha_1,alpha_2,...,alpha_p; beta_1,beta_2,...,beta_q;z] is said to be well-poised if p=q+1 and ...

Legendre's conjecture asserts that for every n there exists a prime p between n^2 and (n+1)^2 (Hardy and Wright 1979, p. 415; Ribenboim 1996, pp. 397-398). It is one of ...

The number of poles of an automorphic function in the closure of its fundamental region.

Let r be the correlation coefficient. Then defining z^'=tanh^(-1)r (1) zeta=tanh^(-1)rho, (2) gives sigma_(z^') = (N-3)^(-1/2) (3) var(z^') = 1/n+(4-rho^2)/(2n^2)+... (4) ...

When f:A->B is a ring homomorphism and b is an ideal in B, then f^(-1)(b) is an ideal in A, called the contraction of b and sometimes denoted b^c. The contraction of a prime ...

The set of prime numbers, sometimes denoted P (Derbyshire 2004, p. 163), and implemented in the Wolfram Language as Primes. In the Wolfram Language, a quantity can be tested ...

An entire function f is said to be of finite order if there exist numbers a,r>0 such that |f(z)|<=exp(|z|^a) for all |z|>r. The infimum of all numbers a for which this ...