Question 64
Find all positive integers $a$ for which there exists a polynomial $p(x)$ with integer coefficients such that
$$
p(\sqrt{2} + 1) = 2 - \sqrt{2} \quad \text{and} \quad p(\sqrt{2} + 2) = a.
$$
$$
p(\sqrt{2} + 1) = 2 - \sqrt{2} \quad \text{and} \quad p(\sqrt{2} + 2) = a.
$$