Displaying similar documents to “Prime graph components of finite almost simple groups”

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 , 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 2 , with P an arbitrary integer, is determined.

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.