Question 90
We call a positive integer *n delightful* if there exists an integer $x$, $1 \lt x \lt n$, such that
$$
1 + 2 + \cdots + (x - 1) = (x + 1) + (x + 2) + \cdots + n.
$$
Does there exist a delightful number *N* satisfying
$$
2013^{2013} \lt \frac{N}{2013^{2013}} \lt 2013^{2013} + 4.
$$
$$
1 + 2 + \cdots + (x - 1) = (x + 1) + (x + 2) + \cdots + n.
$$
Does there exist a delightful number *N* satisfying
$$
2013^{2013} \lt \frac{N}{2013^{2013}} \lt 2013^{2013} + 4.
$$