IT-CESENATICO 2007 Problem 2

We define two polynomials with integer coefficients P,Q to be similar if the coefficients of P are a permutation of the coefficients of Q. a) if P,Q are similar, then $P(2007)-Q(2007)$ is even b) does there exist an integer $k > 2$ such that $k \mid P(2007)-Q(2007)$ for all similar polynomials P,Q?