Question 1
Suppose $f$ is a positive integer-valued function defined for the set of positive integers satisfying for any pair of positive integers $x, y$ the following inequality:
$$
(x + y)f(x) \leq x^2 + f(xy) + 110.
$$
Determine the minimum and the maximum value of $f(23) + f(2011)$ for this $f$.
$$
(x + y)f(x) \leq x^2 + f(xy) + 110.
$$
Determine the minimum and the maximum value of $f(23) + f(2011)$ for this $f$.