Question 48
Find all functions $f : \mathbb{N} \to \mathbb{R}$ ($\mathbb{N}$ denotes the set of all positive integers, $\mathbb{R}$ the set of all real numbers) such that
$$
f(km) + f(kn) - f(k)f(nm) \geq 1
$$
for all $k, m, n \in \mathbb{N}$.
$$
f(km) + f(kn) - f(k)f(nm) \geq 1
$$
for all $k, m, n \in \mathbb{N}$.