Question 19
Let $p(x),q(x)$ be distinct polynomials of degree at most 3 with integer coefficients, such that
$$p(1)=q(1),\quad p(2)=q(2),\quad p(3)=q(3),$$
$$p(-1)=-q(-1),\quad p(-2)=-q(-2),$$
$$p(-3)=-q(-3).$$
What is the least possible value of $[p(0)]^2+[q(0)]^2$?
$$p(1)=q(1),\quad p(2)=q(2),\quad p(3)=q(3),$$
$$p(-1)=-q(-1),\quad p(-2)=-q(-2),$$
$$p(-3)=-q(-3).$$
What is the least possible value of $[p(0)]^2+[q(0)]^2$?