title: 1000 digit number is Fibonacci number or not
body: <p>I was doing a problem on Codechef of November COOK-OFF, in which I have to find whether a given 1000 digit number is Fibonacci number or not. </p>
  
  <p>I know the property that if n is fibonacci number then <code>5n^2 + 4</code> or <code>5n^2 - 4</code> is a perfect square but I found a much simpler approach here.</p>
  
  <p><a href="http://www.codechef.com/viewsolution/2996264" rel="nofollow">http://www.codechef.com/viewsolution/2996264</a></p>
  
  <p>Can anybody please explain me why this is working ???</p>
  
  <p>Here is the link for the question</p>
  
  <p><a href="http://www.codechef.com/COOK40/problems/AMIFIB" rel="nofollow">http://www.codechef.com/COOK40/problems/AMIFIB</a></p>