C++ 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).



filter_none

edit
close

play_arrow

link
brightness_4
code

// C++ program to check if x is a perfect square
#include <iostream>
#include <math.h>
using namespace std;
  
// A utility function that returns true if x is perfect square
bool isPerfectSquare(int x)
{
    int s = sqrt(x);
    return (s * s == x);
}
  
// Returns true if n is a Fibinacci Number, else false
bool isFibonacci(int n)
{
    // n is Fibinacci if one of 5*n*n + 4 or 5*n*n - 4 or both
    // is a perferct square
    return isPerfectSquare(5 * n * n + 4) || isPerfectSquare(5 * n * n - 4);
}
  
// A utility function to test above functions
int main()
{
    for (int i = 1; i <= 10; i++)
        isFibonacci(i) ? cout << i << " is a Fibonacci Number \n"
                       : cout << i << " is a not Fibonacci Number \n";
    return 0;
}

chevron_right


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

Please refer complete article on How to check if a given number is Fibonacci number? for more details!



My Personal Notes arrow_drop_up


Article Tags :

Be the First to upvote.


Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.