Python Program for How to check if a given number is the 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:
# 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 " |
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