Find the number of integers n, 1 < n < 2014, such that 8n/(9999 - n) is also an integer.

For n between 1 and 2014, I could only find one value for n. However, if n is between 1 and 9999, there are well over 40 integers that satisfy your conditions.

n =1,111.

8 x 1,111 =8,888

9999 - 1111 =8,888

So, 8,888 / 8,888 = 1