Python 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, 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! 

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