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Found problems: 1

2021 Tuymaada Olympiad, 8
Tags: polynomial , quadratics , algebra , rational functions
In a sequence $P_n$ of quadratic trinomials each trinomial, starting with the third, is the sum of the two preceding trinomials. The first two trinomials do not have common roots. Is it possible that $P_n$ has an integral root for each $n$?