Question 100
Given two distinct square-free positive integers $a$ and $b$, show that
$$
|\{n\sqrt{a}\} - \{n\sqrt{b}\}| \gt c n^{-3},
$$
for some positive constant $c$ and all positive integers $n$.
$$
|\{n\sqrt{a}\} - \{n\sqrt{b}\}| \gt c n^{-3},
$$
for some positive constant $c$ and all positive integers $n$.