Displaying similar documents to “New prime-producing quadratic polynomials associated with class number one or two.”

Prime factors of values of polynomials

J. Browkin, A. Schinzel (2011)

Colloquium Mathematicae


We prove that for every quadratic binomial f(x) = rx² + s ∈ ℤ[x] there are pairs ⟨a,b⟩ ∈ ℕ² such that a ≠ b, f(a) and f(b) have the same prime factors and min{a,b} is arbitrarily large. We prove the same result for every monic quadratic trinomial over ℤ.

Frobenius distributions for real quadratic orders

Peter Stevenhagen (1995)

Journal de théorie des nombres de Bordeaux


We present a density result for the norm of the fundamental unit in a real quadratic order that follows from an equidistribution assumption for the infinite Frobenius elements in the class groups of these orders.

Lower powers of elliptic units

Stefan Bettner, Reinhard Schertz (2001)

Journal de théorie des nombres de Bordeaux


In the previous paper [Sch2] it has been shown that ray class fields over quadratic imaginary number fields can be generated by simple products of singular values of the Klein form defined below. In the present article the second named author has constructed more general products that are contained in ray class fields thereby correcting Theorem 2 of [Sch2]. An algorithm for the computation of the algebraic equations of the numbers in Theorem 1 of this paper has been implemented in a...

A necessary and sufficient condition for the primality of Fermat numbers

Michal Křížek, Lawrence Somer (2001)

Mathematica Bohemica


We examine primitive roots modulo the Fermat number F m = 2 2 m + 1 . We show that an odd integer n 3 is a Fermat prime if and only if the set of primitive roots modulo n is equal to the set of quadratic non-residues modulo n . This result is extended to primitive roots modulo twice a Fermat number.