The integer
![9](/media/m/7/f/0/7f02ff2403dbf63ddc4395762441de88.png)
can be written as a sum of two consecutive integers:
![9 = 4+5.](/media/m/d/f/e/dfeccce89866ce5b2a2bba7118cad261.png)
Moreover, it can be written as a sum of (more than one) consecutive positive integers in exactly two ways:
![9 = 4+5 = 2+3+4.](/media/m/e/9/f/e9f9e5b420d593b7fa0d12f6b19cdf31.png)
Is there an integer that can be written as a sum of
![1990](/media/m/a/e/f/aefc5b30ee77dec2d8030ec68f1626f9.png)
consecutive integers and that can be written as a sum of (more than one) consecutive positive integers in exactly
![1990](/media/m/a/e/f/aefc5b30ee77dec2d8030ec68f1626f9.png)
ways?
%V0
The integer $9$ can be written as a sum of two consecutive integers: $9 = 4+5.$ Moreover, it can be written as a sum of (more than one) consecutive positive integers in exactly two ways: $9 = 4+5 = 2+3+4.$ Is there an integer that can be written as a sum of $1990$ consecutive integers and that can be written as a sum of (more than one) consecutive positive integers in exactly $1990$ ways?