Question 43
If $d(n)$ is the number of positive divisors of $n$, prove that there exists a natural number $n$ such that:
$$
\forall i \in \mathbb{N},\ i \le 1402 : \frac{d(n)}{d(n \pm i)} \gt 1401.
$$
$$
\forall i \in \mathbb{N},\ i \le 1402 : \frac{d(n)}{d(n \pm i)} \gt 1401.
$$