Check if a Given Number is Fibonacci number?

Last Updated : 23 May, 2026

Given a number n, check if n is a Fibonacci number. First few Fibonacci numbers are 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ..

Examples :

Input: n = 34
Output: true
Explanation: 34 is one of the numbers of the Fibonacci series.

Input: n = 41
Output: false
Explanation: 41 is not in the numbers of the Fibonacci series.

Try It Yourself
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Table of Content

Generate Fibonacci Numbers Iteratively - O(log n) Time O(1) Space

The idea is to generate Fibonacci numbers one by one starting from 0 and 1 until the generated number becomes greater than or equal to n.

  • If the generated Fibonacci number becomes equal to n, then n is a Fibonacci number.
  • Otherwise, n is not a Fibonacci number.
C++
#include <bits/stdc++.h>
using namespace std;

bool isFibonacci(int n)
{

    // Base cases
    if (n == 0 || n == 1)
    {
        return true;
    }

    int a = 0;
    int b = 1;
    int c = a + b;

    // Generate Fibonacci numbers
    while (c < n)
    {
        a = b;
        b = c;
        c = a + b;
    }

    return c == n;
}

// Driver Code
int main()
{
    int n = 34;

    if (isFibonacci(n))
    {
        cout << "true";
    }
    else
    {
        cout << "false";
    }

    return 0;
}
Java
public class GfG {

    public static boolean isFibonacci(int n)
    {

        // Base cases
        if (n == 0 || n == 1)
        {
            return true;
        }

        int a = 0;
        int b = 1;
        int c = a + b;

        // Generate Fibonacci numbers
        while (c < n)
        {
            a = b;
            b = c;
            c = a + b;
        }

        return c == n;
    }

    // Driver Code
    public static void main(String[] args)
    {
        int n = 34;

        if (isFibonacci(n))
        {
            System.out.println("true");
        }
        else
        {
            System.out.println("false");
        }
    }
}
Python
def isFibonacci(n):

    # Base cases
    if n == 0 or n == 1:
        return True

    a = 0
    b = 1
    c = a + b

    # Generate Fibonacci numbers
    while c < n:
        a = b
        b = c
        c = a + b

    return c == n

# Driver Code
if __name__ == '__main__':
    n = 34

    if isFibonacci(n):
        print('true')
    else:
        print('false')
C#
using System;

public class GfG
{
    public static bool IsFibonacci(int n)
    {

        // Base cases
        if (n == 0 || n == 1)
        {
            return true;
        }

        int a = 0;
        int b = 1;
        int c = a + b;

        // Generate Fibonacci numbers
        while (c < n)
        {
            a = b;
            b = c;
            c = a + b;
        }

        return c == n;
    }

    // Driver Code
    public static void Main()
    {
        int n = 34;

        if (IsFibonacci(n))
        {
            Console.WriteLine("true");
        }
        else
        {
            Console.WriteLine("false");
        }
    }
}
JavaScript
function isFibonacci(n) {

    // Base cases
    if (n == 0 || n == 1) {
        return true;
    }

    let a = 0;
    let b = 1;
    let c = a + b;

    // Generate Fibonacci numbers
    while (c < n) {
        a = b;
        b = c;
        c = a + b;
    }

    return c == n;
}

// Driver Code
let n = 34;

if (isFibonacci(n)) {
    console.log('true');
} else {
    console.log('false');
}

Output
true

Time Complexity: O(log n)
Space Complexity: O(1)

Using Perfect Square Property - O(1) Time O(1) Space

A number n is a Fibonacci number if either of the following is a perfect square: 5n2 + 4 or 5n2 − 4. So, we calculate both values and check if any one of them is a perfect square. If any one of them is a perfect square, then n is a Fibonacci number.

This is a mathematical property of Fibonacci numbers: 5n2 + 4 or 5n2 − 4.

C++
#include <bits/stdc++.h>
using namespace std;

// Check if x is a perfect square
bool isPerfectSquare(int x)
{
    int s = sqrt(x);

    return s * s == x;
}

// Check if n is a Fibonacci number
bool isFibonacci(int n)
{
    int val1 = 5 * n * n + 4;
    int val2 = 5 * n * n - 4;

    return isPerfectSquare(val1) || isPerfectSquare(val2);
}

int main()
{
    int n = 34;

    if (isFibonacci(n))
        cout << "true";
    else
        cout << "false";

    return 0;
}
Java
import java.lang.Math;

// Check if x is a perfect square
public class GfG {
    public static boolean isPerfectSquare(int x)
    {
        int s = (int) Math.sqrt(x);

        return s * s == x;
    }

    // Check if n is a Fibonacci number
    public static boolean isFibonacci(int n)
    {
        int val1 = 5 * n * n + 4;
        int val2 = 5 * n * n - 4;

        return isPerfectSquare(val1) || isPerfectSquare(val2);
    }

    public static void main(String[] args)
    {
        int n = 34;

        if (isFibonacci(n))
            System.out.println("true");
        else
            System.out.println("false");
    }
}
Python
import math

# Check if x is a perfect square
def isPerfectSquare(x):
    s = int(math.sqrt(x))

    return s * s == x

# Check if n is a Fibonacci number
def isFibonacci(n):
    val1 = 5 * n * n + 4
    val2 = 5 * n * n - 4
    return isPerfectSquare(val1) or isPerfectSquare(val2)

n = 34
if isFibonacci(n):
    print("true")
else:
    print("false")
C#
using System;

// Check if x is a perfect square
public class GfG
{
    public static bool isPerfectSquare(int x)
    {
        int s = (int)Math.Sqrt(x);

        return s * s == x;
    }

    // Check if n is a Fibonacci number
    public static bool isFibonacci(int n)
    {
        int val1 = 5 * n * n + 4;
        int val2 = 5 * n * n - 4;

        return isPerfectSquare(val1) || isPerfectSquare(val2);
    }

    public static void Main()
    {
        int n = 34;

        if (isFibonacci(n))
            Console.WriteLine("true");
        else
            Console.WriteLine("false");
    }
}
JavaScript
// Check if x is a perfect square
function isPerfectSquare(x) {
    let s = Math.sqrt(x);

    return s * s === x;
}

// Check if n is a Fibonacci number
function isFibonacci(n) {
    let val1 = 5 * n * n + 4;
    let val2 = 5 * n * n - 4;

    return isPerfectSquare(val1) || isPerfectSquare(val2);
}

let n = 34;

if (isFibonacci(n)) {
    console.log('true');
} else {
    console.log('false');
}

Output
true

Time Complexity: O(1)
Space Complexity: O(1)

Comment
Article Tags:
Mathematical
DSA
MAQ Software
Fibonacci

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