package Maths;

/**
 * Fibonacci: 0 1 1 2 3 5 8 13 21 ...
 */
public class FibonacciNumber {
 public static void main(String[] args) {
 assert isFibonacciNumber(1);
 assert isFibonacciNumber(2);
 assert isFibonacciNumber(21);
 assert !isFibonacciNumber(9);
 assert !isFibonacciNumber(10);
 }

 /**
 * Check if a number is perfect square number
 *
 * @param number the number to be checked
 * @return <tt>true</tt> if {@code number} is perfect square, otherwise <tt>false</tt>
 */
 public static boolean isPerfectSquare(int number) {
 int sqrt = (int) Math.sqrt(number);
 return sqrt * sqrt == number;
 }

 /**
 * Check if a number is fibonacci number
 * This is true if and only if at least one of 5x^2+4 or 5x^2-4 is a perfect square
 *
 * @param number the number
 * @return <tt>true</tt> if {@code number} is fibonacci number, otherwise <tt>false</tt>
 * @link https://en.wikipedia.org/wiki/Fibonacci_number#Identification
 */
 public static boolean isFibonacciNumber(int number) {
 return isPerfectSquare(5 * number * number + 4) || isPerfectSquare(5 * number * number - 4);
 }
}