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Christian Ballot and Florian Luca
Prime factors of af(n)-1 with an irreducible polynomial f(x)
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| Published: |
April 12, 2006
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| Keywords: |
Prime factors, linear recurrences, Chebotarev Density Theorem |
| Subject: |
11N37, 11B37 |
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Abstract
In this note, we show that if a is an integer not 0 or ±1
and f(X)∈ Q[X] is an integer valued irreducible polynomial
of degree d≧ 2, then the set of primes p dividing
af(n)-1 for some positive integer n is of (relative)
asymptotic density zero.
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| Acknowledgements
This paper was written during a very enjoyable visit by the second author to the Laboratoire Nicolas Oresme of the University of Caen; he wishes to express his thanks to that institution for its hospitality and support. He was also partly supported by grants SEP-CONACYT 46755, PAPIIT IN104505 and a Guggenheim Fellowship.
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| Author information
Christian Ballot:
Laboratoire de Mathématiques Nicolas Oresme, Université de Caen, BP 5186, 14032 Caen Cedex, France
Christian.Ballot@math.unicaen.fr
Florian Luca:
Instituto de Matemáticas, Universidad Nacional Autonoma de México, C.P. 58089, Morelia, Michoacán, México
fluca@matmor.unam.mx
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