Towards Bauer's theorem for linear recurrence sequences
Mariusz Skałba
Colloquium Mathematicae, Tome 96 (2003), p. 163-169 / Harvested from The Polish Digital Mathematics Library
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Consider a recurrence sequence (xk)k∈ℤ of integers satisfying xk+n=an-1xk+n-1+...+a₁xk+1+a₀xk, where a₀,a₁,...,an-1∈ℤ are fixed and a₀ ∈ -1,1. Assume that xk>0 for all sufficiently large k. If there exists k₀∈ ℤ such that xk₀<0 then for each negative integer -D there exist infinitely many rational primes q such that q|xk for some k ∈ ℕ and (-D/q) = -1.

Publié le : 2003-01-01
EUDML-ID : urn:eudml:doc:284925 
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     year = {2003},
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Mariusz Skałba. Towards Bauer's theorem for linear recurrence sequences. Colloquium Mathematicae, Tome 96 (2003) pp. 163-169. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm98-2-3/