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Towards Bauer's theorem for linear recurrence sequences

Mariusz Skałba (2003)

Colloquium Mathematicae

Consider a recurrence sequence ( x k ) k ∈ ℤ of integers satisfying x k + n = a n - 1 x k + n - 1 + . . . + a ₁ x k + 1 + a ₀ x k , where a ₀ , a ₁ , . . . , a n - 1 ∈ ℤ are fixed and a₀ ∈ -1,1. Assume that x k > 0 for all sufficiently large k. If there exists k₀∈ ℤ such that x k ₀ < 0 then for each negative integer -D there exist infinitely many rational primes q such that q | x k for some k ∈ ℕ and (-D/q) = -1.

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