Prime divisors of Lucas sequences

Pieter Moree; Peter Stevenhagen

Displaying similar documents to “Prime divisors of Lucas sequences”

On the prime density of Lucas sequences

Pieter Moree (1996)

Journal de théorie des nombres de Bordeaux

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The density of primes dividing at least one term of the Lucas sequence ${\{L_{n} (P)\}}_{n = 0}^{\infty}$ , defined by $L_{0} (P) = 2, L_{1} (P) = P$ and $L_{n} (P) = P L_{n - 1} (P) + L_{n - 2} (P)$ for $n \geq 2$ , with $P$ an arbitrary integer, is determined.

Computations of Iwasawa invariants and $𝐊_{2}$

Alan Candiotti (1974)

Compositio Mathematica

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A problem of Erdös concerning power residue sums.

P. Elliott (1967)

Acta Arithmetica

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Unramified quaternion extensions of quadratic number fields

Franz Lemmermeyer (1997)

Journal de théorie des nombres de Bordeaux

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Classical results of Rédei, Reichardt and Scholz show that unramified cyclic quartic extensions of quadratic number fields $k$ correspond to certain factorizations of its discriminant disc $k$ . In this paper we extend their results to unramified quaternion extensions of $k$ which are normal over $ℚ$ , and show how to construct them explicitly.

Initial layers of $Z_{l}$ -extensions of complex quadratic fields

J. E. Carroll, H. Kisilevsky (1976)

Compositio Mathematica

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On determining the quadratic subfields of $Z_{2}$ -extensions of complex quadratic fields

Joseph E. Carroll (1975)

Compositio Mathematica

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Class number parity of a compositum of five quadratic fields

Michal Bulant (2002)

Acta Mathematica et Informatica Universitatis Ostraviensis

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A quadratic field of prime discriminant requiring three generators for its class group, and related theory

Daniel Shanks, Peter Weinberger (1972)

Acta Arithmetica

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Artin's primitive root conjecture for quadratic fields

Hans Roskam (2002)

Journal de théorie des nombres de Bordeaux

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Fix an element $α$ in a quadratic field $K$ . Define $S$ as the set of rational primes $p$ , for which $α$ has maximal order modulo $p$ . Under the assumption of the generalized Riemann hypothesis, we show that $S$ has a density. Moreover, we give necessary and sufficient conditions for the density of $S$ to be positive.