Question

Problem 3 Fibonacci Numbers 10 points Fibonacci numbers are a sequence of numbers where each number is represented by the sum of the two preceding numbers, starting with 0 and 1: 0, 1, 1, 2, 3, 5, 8, etc Write a program that repeatedly prompts the user for a positive integer and prints out whether or not that integer is a Fibonacci number. The program terminates when-I is entered. Create a method with the following signature. The method tests whether the number passed to it is a Fibonacci number or not. It returns true if the number is indeed a Fibonacci number and it returns false otherwise. bool isFibonacci(int number) Example: Input: 21 Output: 21 is a Fibonacci number Input: 9 Output: 9 is not a Fibonacci number Input: -1 Goodbye!

Question 3 Program Language C++

Answer 1

A very nice test is that N is a Fibonacci number if and only if 5 N^2 + 4 or 5N^2 – 4 is a square number.

code

=========================================================================

// C++ program to check if x is a perfect square
#include <iostream>
#include <math.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 Fibinacci Number, else false
bool isFibonacci(int number)
{
// n is Fibinacci if one of 5*n*n + 4 or 5*n*n - 4 or both
// is a perferct square
return isPerfectSquare(5*number*number + 4) ||
isPerfectSquare(5*number*number - 4);
}

// A utility function to test above functions
int main()
{
int n;
cout<<"Enter the inputs :\n";
for(int i=0;i<=100;i++)

{  
bool result=true;
cout<<"Input: ";
cin>>n;
if(n>0)
{
if(isFibonacci(n) == result)
{
cout<<n << " is fibonacci number\n";
}
else
{
cout<<n <<" is not a fibonacci number\n";
}
}
else
{

cout<<n<<" Goodbye \n";
break;
}
  
}
  
return 0;
}

===================================================================================

Hope this will help.

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