MathDB

The sequence Pn (x), n ∈ N of polynomials is defined as follows: P0 (x) = x, P1 (x) = 4x³ + 3x Pn+1 (x) = (4x² + 2)Pn (x) − Pn−1 (x), for all n ≥ 1 For every positive integer m, we consider the set A(m) = { Pn (m) | n ∈ N }. Show that the sets A(m) and A(m+4) have no common elements.

Problem Statement