Question 41
Find all functions $f$ on the positive integers with positive integer values such that
(1) if $x \lt y$, then $f(x) \lt f(y)$, and
(2) $f(y f(x)) = x^{2} f(x y)$.
(1) if $x \lt y$, then $f(x) \lt f(y)$, and
(2) $f(y f(x)) = x^{2} f(x y)$.