Given $n$ and $k$, find the number of pairs of integers $(a, b)$ which satisfy the conditions $n < a < k, n < b < k$ and $(ab-n)$ is divisible by $(a-n)(b-n)$. Given: $0 ≤ n ≤ 100000, \ n < k ≤ 10^{18}$.
Link to problem: http://www.codechef.com/SEPT11/problems/SHORT