MathNet 2017-part-07 — 172 problems (EN–VI) Question 45

For positive integers $a$ and $N$, let $r(a, N) \in \{0,1, \ldots, N-1\}$ denote the remainder of $a$ when divided by $N$. Determine the number of positive integers $n \leq 1000000$ for which
$$
r(n, 1000)\gt r(n, 1001)
$$