ISL 2015 A6

Let $n$ be a fixed integer with $n \geqslant 2$. 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 $$\begin{aligned} & P(2015 i), P(2015 i-1), \ldots, P(2015 i-2014) \text { and } \\ & Q(2015 i), Q(2015 i-1), \ldots, Q(2015 i-2014) \end{aligned}$$ 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 $n$.