Skip to content
Related Articles

Related Articles

Python Program for How to check if a given number is Fibonacci number?

Improve Article
Save Article
  • Difficulty Level : Easy
  • Last Updated : 08 Aug, 2022
Improve Article
Save Article

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, 144, .. 
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). 

Python3




# python program to check if x is a perfect square
import math
 
# A utility function that returns true if x is perfect square
 
 
def isPerfectSquare(x):
    s = int(math.sqrt(x))
    return s*s == x
 
# Returns true if n is a Fibonacci Number, else false
 
 
def isFibonacci(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) or isPerfectSquare(5*n*n - 4)
 
 
# A utility function to test above functions
for i in range(1, 11):
    if (isFibonacci(i) == True):
        print(i, "is a Fibonacci Number")
    else:
        print(i, "is a not Fibonacci Number ")

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 

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

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

My Personal Notes arrow_drop_up
Related Articles

Start Your Coding Journey Now!