Java Program for How to check if a given number is Fibonacci number?
Given a number ‘n’, how to check if n is a Fibonacci number. First few Fibonacci numbers are 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 141, ..
Examples :
Input : 8 Output : Yes Input : 34 Output : Yes Input : 41 Output : No
Following is an interesting property about Fibonacci numbers that can also be used to check if a given number is Fibonacci or not.
A number is Fibonacci if and only if one or both of (5*n2 + 4) or (5*n2 – 4) is a perfect square (Source: Wiki).
// Java program to check if x is a perfect square class GFG { // A utility method that returns true if x is perfect square static boolean isPerfectSquare( int x) { int s = ( int )Math.sqrt(x); return (s * s == x); } // Returns true if n is a Fibonacci Number, else false static boolean isFibonacci( int n) { // n is Fibonacci if one of 5*n*n + 4 or 5*n*n - 4 or both // is a perfect square return isPerfectSquare( 5 * n * n + 4 ) || isPerfectSquare( 5 * n * n - 4 ); } // Driver method public static void main(String[] args) { for ( int i = 1 ; i <= 10 ; i++) System.out.println(isFibonacci(i) ? i + " is a Fibonacci Number" : i + " is a not Fibonacci Number" ); } } // This code is contributed by Nikita Tiwari |
Output:
1 is a Fibonacci Number 2 is a Fibonacci Number 3 is a Fibonacci Number 4 is a not Fibonacci Number 5 is a Fibonacci Number 6 is a not Fibonacci Number 7 is a not Fibonacci Number 8 is a Fibonacci Number 9 is a not Fibonacci Number 10 is a not Fibonacci Number
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