title: Sample testcase for Interviewstreet: Equations
body: <p>So there is a website named interviewstreet.com. Here we can find challenging programming problems. Unfortunately you have to be logged in to see the questions.</p>
  
  <p>Here's a brief description of the problem I'm attempting to solve:</p>
  
  <blockquote>
    <p>Find the no of positive integral solutions for the equations <code>(1/x) + (1/y) = 1/N!</code> (read 1 by n factorial) Print a single integer which is the no of positive integral solutions modulo 1000007.</p>
  </blockquote>
  
  <p>For example, when <code>N=3</code>, <code>(x,y)</code> can be: <code>(7,42)</code>, <code>(9,18)</code>, <code>(8,24)</code>, <code>(12,12)</code>, <code>(42,7)</code>, <code>(18,9)</code>, <code>(24,8)</code>. Or so I thought.</p>
  
  <p>Help me please, especially you who have solved this problem. I have just coded for the problem Equations. There is something wrong with my algorithm, can I ask for output for the first 10 integers? i.e. <code>N=2</code>, <code>N=3</code>, <code>N=4</code> ... <code>N=10</code> so that I can find out the flaw in my algorithm. Thanks :)</p>
  
  <p>EDIT: Oh, please don't post solution code as it will ruin the fun for me and for people trying to solve this :)</p>