In the following equation x, y, and n are positive integers.
1/<var>x</var> + 1/<var>y</var> = 1/<var>n</var>
It can be verified that when <var>n</var> = 1260 there are 113 distinct solutions and this is the least value of <var>n</var> for which the total number of distinct solutions exceeds one hundred.
What is the least value of <var>n</var> for which the number of distinct solutions exceeds four million?