Fibonacci number.txt

 FIBONACCI NUMBERS

The Fibonacci numbers are the numbers in the following integer sequence.
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ……..

In mathematical terms, the sequence Fn of Fibonacci numbers is defined by the recurrence relation

Fn = Fn-1 + Fn-2
with seed values 

F0 = 0 and F1 = 1.
............................................... C PROGRAM.......................................................................

// C program to check if x is a perfect square
#include <math.h>
#include <stdbool.h>
#include <stdio.h>
 
// A utility function that returns true if x is perfect
// square
bool isPerfectSquare(int x)
{
    int s = sqrt(x);
    return (s * s == x);
}
 
// Returns true if n is a Fibonacci Number, else false
bool isFibonacci(int 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)
           || isPerfectSquare(5 * n * n - 4);
}
 
// A utility function to test above functions
int main()
{
    for (int i = 1; i <= 10; i++) {
        if (isFibonacci(i))
            printf("%d is a Fibonacci Number \n", i);
        else
            printf("%d is a not Fibonacci Number \n", i);
    }
    return 0;
}


................................................C++ PROGRAM......................................................


// C++ program to check if x is a perfect square
#include <bits/stdc++.h>
using namespace std;
 
// A utility function that returns true if x is perfect
// square
bool isPerfectSquare(int x)
{
    int s = sqrt(x);
    return (s * s == x);
}
 
// Returns true if n is a Fibonacci Number, else false
bool isFibonacci(int 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)
           || isPerfectSquare(5 * n * n - 4);
}
 
// A utility function to test above functions
int main()
{
    for (int i = 1; i <= 10; i++)
        isFibonacci(i)
            ? cout << i << " is a Fibonacci Number \n"
            : cout << i << " is a not Fibonacci Number \n";
    return 0;
}

..............................................PYTHON PROGRAM.........................................................

# 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 "


.......................................................JAVA PROGRAM.....................................................


// Java program to check if x is a perfect square
 
class Hactoberfest
{
    // A utility method that returns true if x is perfect square
    static  boolean isPerfectSquare(int x)
    {
        int s = (int) Math.sqrt(x);
        return (s*s == x);
    }
      
    // Returns true if n is a Fibonacci Number, else false
    static boolean isFibonacci(int 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) ||
               isPerfectSquare(5*n*n - 4);
    }
 
    // Driver method
    public static void main(String[] args)
    {
        for (int i = 1; i <= 10; i++)
             System.out.println(isFibonacci(i) ?  i +  " is a Fibonacci Number" :
                                                  i + " is a not Fibonacci Number");
    }
}