Question 155
Find all the positive integers $m$ such that there exist polynomials with real coefficients $P(x)$, $Q(x)$, and $R(x, y)$, satisfying the following condition:
$$
P(R(a, b)) = a \text{ and } Q(R(a, b)) = b
$$
for all real numbers $a, b$ such that $a^m - b^2 = 0$.
$$
P(R(a, b)) = a \text{ and } Q(R(a, b)) = b
$$
for all real numbers $a, b$ such that $a^m - b^2 = 0$.