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, 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).

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# 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 Fibinacci Number, else false
def isFibonacci(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) 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 "

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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!



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