VN-TST 2008 Problem 2

Find all values of the positive integer $m$ such that there exists polynomials $P(x),Q(x),R(x,y)$ with real coefficient satisfying the condition: For every real numbers $a,b$ which satisfying $a^m-b^2=0$ , we always have that $P(R(a,b))=a$ and $Q(R(a,b))=b$ .