Question 42
A polynomial $P$ with integer coefficients satisfies
$$
P(x_1) = P(x_2) = \dots = P(x_k) = 54
$$
and
$$
P(y_1) = P(y_2) = \dots = P(y_n) = 2013
$$
for distinct integers $x_1, \dots, x_k; y_1, \dots, y_n$. Determine the maximal value of $kn$.
$$
P(x_1) = P(x_2) = \dots = P(x_k) = 54
$$
and
$$
P(y_1) = P(y_2) = \dots = P(y_n) = 2013
$$
for distinct integers $x_1, \dots, x_k; y_1, \dots, y_n$. Determine the maximal value of $kn$.