MathDB

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
\begin{eqnarray*} P(2015i), P(2015i - 1), \ldots, P(2015i - 2014) & \text{and}\\ Q(2015i), Q(2015i - 1), \ldots, Q(2015i - 2014) \end{eqnarray*}
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

.
Proposed by David Arthur, Canada

Problem Statement