# Problem 110: Diophantine reciprocals II

![graphic](img110.gif)

In the following equation x, y, and n are positive integers. 1x + 1y =
1n It can be verified that when n = 1260 there are 113 distinct
solutions and this is the least value of n for which the total number of
distinct solutions exceeds one hundred. What is the least value of n for
which the number of distinct solutions exceeds four million? NOTE: This
problem is a much more difficult version of Problem 108 and as it is
well beyond the limitations of a brute force approach it requires a
clever implementation.