Question 43
Find all functions $f: \mathbb{N} \to \mathbb{R}$ that satisfy the equation
$$
f(x + y) = f(x) + f(y)
$$
for all $x, y \in \mathbb{N}$ such that $10^6 - 10^{-6} \lt \frac{x}{y} \lt 10^6 + 10^{-6}$.
$$
f(x + y) = f(x) + f(y)
$$
for all $x, y \in \mathbb{N}$ such that $10^6 - 10^{-6} \lt \frac{x}{y} \lt 10^6 + 10^{-6}$.