### IMO Shortlist 2015 problem A6

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30. kolovoza 2018.

Let $n$ be a fixed integer with $n \ge 2$. We say that two polynomials $P$ and $Q$ with real coefficients are block-similar if for each $i \in \{1, 2, \ldots, n\}$ the sequences

$P(2015i), P(2015i - 1), \ldots, P(2015i - 2014) \quad \mbox{and}$
$Q(2015i), Q(2015i - 1), \ldots, Q(2015i - 2014)$

are permutations of each other.

(a) Prove that there exist distinct block-similar polynomials of degree $n + 1$.
(b) Prove that there do not exist distinct block-similar polynomials of degree $n$.