EN
Consider a recurrence sequence $(x_{k})_{k∈ℤ}$ of integers satisfying $x_{k+n} = a_{n-1}x_{k+n-1} + ... + a₁x_{k+1} + a₀x_{k}$, where $a₀,a₁,...,a_{n-1} ∈ ℤ$ are fixed and a₀ ∈ {-1,1}. Assume that $x_{k} > 0$ for all sufficiently large k. If there exists k₀∈ ℤ such that $x_{k₀} < 0$ 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.