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Algebra Difficulty 7.0 National Olympiad, round 2 Find the answer Hungary

Find all triples $(a,b,c)$ of real numbers for which there exists a function $f\colon \mathbb{Z}^+ \to \mathbb{Z}^+$ satisfying $af(n)+bf(n+1)+cf(n+2)<0$ for every $n \in \mathbb{Z}^+$ ( $\mathbb{Z}^{+}$ denotes the set of positive integers).

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