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Code Mathematics

Determine that if given number is Fibonacci Number

A Fibonacci number is a number in the sequence of Fibonacci numbers, which is defined as follows:

  • The first two Fibonacci numbers are 0 and 1.
  • Each subsequent Fibonacci number is the sum of the two preceding Fibonacci numbers.

So, for example, the first few Fibonacci numbers are: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, and so on.

To determine if a given number is a Fibonacci number, you can check if it can be expressed as the sum of two preceding Fibonacci numbers. One way to do this is to use the following formula:

  • A number N is a Fibonacci number if and only if 5N^2 + 4 or 5N^2 - 4 is a perfect square.

If either of these expressions is a perfect square, then N is a Fibonacci number. Otherwise, it is not.

For example, let's say we want to determine if the number 8 is a Fibonacci number. Using the formula above, we get:

  • 5(8)^2 + 4 = 324, which is a perfect square (18^2)
  • 5(8)^2 - 4 = 316, which is not a perfect square

Therefore, 8 is a Fibonacci number.

Program Solution

//  C program for
//  Determine that if given number is Fibonacci Number
#include <stdio.h>

#include <math.h>

void isFibonacciNo(int n)
{
	//  5n²+4
	int a = 5 *n *n + 4;
	//  5n²-4
	int b = 5 *n *n - 4;
	int aSqrt = sqrt(a);
	int bSqrt = sqrt(b);
	if ((aSqrt *aSqrt) == a || (bSqrt *bSqrt) == b)
	{
		// When aSqrt or bSqrt is perfect square
		printf("\n Given %d is fibonacci number ", n);
	}
	else
	{
		printf("\n Given %d is not fibonacci number ", n);
	}
}
int main(int argc, char
	const *argv[])
{
	isFibonacciNo(51);
	isFibonacciNo(144);
	isFibonacciNo(987);
	isFibonacciNo(14);
	return 0;
}

Output

 Given 51 is not fibonacci number
 Given 144 is fibonacci number
 Given 987 is fibonacci number
 Given 14 is not fibonacci number
// Java Program 
// Determine that if given number is Fibonacci Number
public class FibonacciNumber
{
	public void isFibonacciNo(int n)
	{
		//  5n²+4
		int a = 5 * n * n + 4;
		//  5n²-4
		int b = 5 * n * n - 4;
		int aSqrt = (int) Math.sqrt(a);
		int bSqrt = (int) Math.sqrt(b);
		if ((aSqrt * aSqrt) == a || (bSqrt * bSqrt) == b)
		{
			// When aSqrt or bSqrt is perfect square
			System.out.print("\n Given " + n + " is fibonacci number ");
		}
		else
		{
			System.out.print("\n Given " + n + " is not fibonacci number ");
		}
	}
	public static void main(String[] args)
	{
		FibonacciNumber task = new FibonacciNumber();
		// Test
		task.isFibonacciNo(51);
		task.isFibonacciNo(144);
		task.isFibonacciNo(987);
		task.isFibonacciNo(14);
	}
}

Output

 Given 51 is not fibonacci number
 Given 144 is fibonacci number
 Given 987 is fibonacci number
 Given 14 is not fibonacci number
// Include header file
#include <iostream>
#include <math.h>
using namespace std;

// C++ Program 
// Determine that if given number is Fibonacci Number
class FibonacciNumber
{
	public: void isFibonacciNo(int n)
	{
		//  5n²+4
		int a = 5 *n *n + 4;
		//  5n²-4
		int b = 5 *n *n - 4;
		int aSqrt = (int) sqrt(a);
		int bSqrt = (int) sqrt(b);
		if ((aSqrt *aSqrt) == a || (bSqrt *bSqrt) == b)
		{
			// When aSqrt or bSqrt is perfect square
			cout << "\n Given " << n << " is fibonacci number ";
		}
		else
		{
			cout << "\n Given " << n << " is not fibonacci number ";
		}
	}
};
int main()
{
	FibonacciNumber *task = new FibonacciNumber();
	// Test
	task->isFibonacciNo(51);
	task->isFibonacciNo(144);
	task->isFibonacciNo(987);
	task->isFibonacciNo(14);
	return 0;
}

Output

 Given 51 is not fibonacci number
 Given 144 is fibonacci number
 Given 987 is fibonacci number
 Given 14 is not fibonacci number
// Include namespace system
using System;
// Csharp Program 
// Determine that if given number is Fibonacci Number
public class FibonacciNumber
{
	public void isFibonacciNo(int n)
	{
		//  5n²+4
		int a = 5 * n * n + 4;
		//  5n²-4
		int b = 5 * n * n - 4;
		int aSqrt = (int) Math.Sqrt(a);
		int bSqrt = (int) Math.Sqrt(b);
		if ((aSqrt * aSqrt) == a || (bSqrt * bSqrt) == b)
		{
			// When aSqrt or bSqrt is perfect square
			Console.Write("\n Given " + n + " is fibonacci number ");
		}
		else
		{
			Console.Write("\n Given " + n + " is not fibonacci number ");
		}
	}
	public static void Main(String[] args)
	{
		FibonacciNumber task = new FibonacciNumber();
		// Test
		task.isFibonacciNo(51);
		task.isFibonacciNo(144);
		task.isFibonacciNo(987);
		task.isFibonacciNo(14);
	}
}

Output

 Given 51 is not fibonacci number
 Given 144 is fibonacci number
 Given 987 is fibonacci number
 Given 14 is not fibonacci number
package main
import "math"
import "fmt"
// Go Program 
// Determine that if given number is Fibonacci Number

func isFibonacciNo(n int) {
	//  5n²+4
	var a int = 5 * n * n + 4
	//  5n²-4
	var b int = 5 * n * n - 4
	var aSqrt int = int(math.Sqrt(float64(a)))
	var bSqrt int = int(math.Sqrt(float64(b)))
	if (aSqrt * aSqrt) == a || (bSqrt * bSqrt) == b {
		// When aSqrt or bSqrt is perfect square
		fmt.Print("\n Given ", n, " is fibonacci number ")
	} else {
		fmt.Print("\n Given ", n, " is not fibonacci number ")
	}
}
func main() {
	
	// Test
	isFibonacciNo(51)
	isFibonacciNo(144)
	isFibonacciNo(987)
	isFibonacciNo(14)
}

Output

 Given 51 is not fibonacci number
 Given 144 is fibonacci number
 Given 987 is fibonacci number
 Given 14 is not fibonacci number
<?php
// Php Program 
// Determine that if given number is Fibonacci Number
class FibonacciNumber
{
	public	function isFibonacciNo($n)
	{
		//  5n²+4
		$a = 5 * $n * $n + 4;
		//  5n²-4
		$b = 5 * $n * $n - 4;
		$aSqrt = (int) sqrt($a);
		$bSqrt = (int) sqrt($b);
		if (($aSqrt * $aSqrt) == $a || ($bSqrt * $bSqrt) == $b)
		{
			// When aSqrt or bSqrt is perfect square
			echo("\n Given ".$n.
				" is fibonacci number ");
		}
		else
		{
			echo("\n Given ".$n.
				" is not fibonacci number ");
		}
	}
}

function main()
{
	$task = new FibonacciNumber();
	// Test
	$task->isFibonacciNo(51);
	$task->isFibonacciNo(144);
	$task->isFibonacciNo(987);
	$task->isFibonacciNo(14);
}
main();

Output

 Given 51 is not fibonacci number
 Given 144 is fibonacci number
 Given 987 is fibonacci number
 Given 14 is not fibonacci number
// Node JS Program 
// Determine that if given number is Fibonacci Number
class FibonacciNumber
{
	isFibonacciNo(n)
	{
		//  5n²+4
		var a = 5 * n * n + 4;
		//  5n²-4
		var b = 5 * n * n - 4;
		var aSqrt = parseInt(Math.sqrt(a));
		var bSqrt = parseInt(Math.sqrt(b));
		if ((aSqrt * aSqrt) == a || (bSqrt * bSqrt) == b)
		{
			// When aSqrt or bSqrt is perfect square
			process.stdout.write("\n Given " + n + " is fibonacci number ");
		}
		else
		{
			process.stdout.write("\n Given " + n + " is not fibonacci number ");
		}
	}
}

function main()
{
	var task = new FibonacciNumber();
	// Test
	task.isFibonacciNo(51);
	task.isFibonacciNo(144);
	task.isFibonacciNo(987);
	task.isFibonacciNo(14);
}
main();

Output

 Given 51 is not fibonacci number
 Given 144 is fibonacci number
 Given 987 is fibonacci number
 Given 14 is not fibonacci number
import math
#  Python 3 Program 
#  Determine that if given number is Fibonacci Number
class FibonacciNumber :
	def isFibonacciNo(self, n) :
		#   5n²+4
		a = 5 * n * n + 4
		#   5n²-4
		b = 5 * n * n - 4
		aSqrt = int(math.sqrt(a))
		bSqrt = int(math.sqrt(b))
		if ((aSqrt * aSqrt) == a or(bSqrt * bSqrt) == b) :
			#  When aSqrt or bSqrt is perfect square
			print("\n Given ", n ," is fibonacci number ", end = "")
		else :
			print("\n Given ", n ," is not fibonacci number ", end = "")
		
	

def main() :
	task = FibonacciNumber()
	#  Test
	task.isFibonacciNo(51)
	task.isFibonacciNo(144)
	task.isFibonacciNo(987)
	task.isFibonacciNo(14)

if __name__ == "__main__": main()

Output

 Given  51  is not fibonacci number
 Given  144  is fibonacci number
 Given  987  is fibonacci number
 Given  14  is not fibonacci number
#  Ruby Program 
#  Determine that if given number is Fibonacci Number
class FibonacciNumber 
	def isFibonacciNo(n) 
		#   5n²+4
		a = 5 * n * n + 4
		#   5n²-4
		b = 5 * n * n - 4
		aSqrt = Math.sqrt(a).to_i
		bSqrt = Math.sqrt(b).to_i
		if ((aSqrt * aSqrt) == a || (bSqrt * bSqrt) == b) 
			#  When aSqrt or bSqrt is perfect square
			print("\n Given ", n ," is fibonacci number ")
		else
 
			print("\n Given ", n ," is not fibonacci number ")
		end

	end

end

def main() 
	task = FibonacciNumber.new()
	#  Test
	task.isFibonacciNo(51)
	task.isFibonacciNo(144)
	task.isFibonacciNo(987)
	task.isFibonacciNo(14)
end

main()

Output

 Given 51 is not fibonacci number 
 Given 144 is fibonacci number 
 Given 987 is fibonacci number 
 Given 14 is not fibonacci number 
// Scala Program 
// Determine that if given number is Fibonacci Number
class FibonacciNumber()
{
	def isFibonacciNo(n: Int): Unit = {
		//  5n²+4
		var a: Int = 5 * n * n + 4;
		//  5n²-4
		var b: Int = 5 * n * n - 4;
		var aSqrt: Int = scala.math.sqrt(a).toInt;
		var bSqrt: Int = scala.math.sqrt(b).toInt;
		if ((aSqrt * aSqrt) == a || (bSqrt * bSqrt) == b)
		{
			// When aSqrt or bSqrt is perfect square
			print("\n Given " + n + " is fibonacci number ");
		}
		else
		{
			print("\n Given " + n + " is not fibonacci number ");
		}
	}
}
object Main
{
	def main(args: Array[String]): Unit = {
		var task: FibonacciNumber = new FibonacciNumber();
		// Test
		task.isFibonacciNo(51);
		task.isFibonacciNo(144);
		task.isFibonacciNo(987);
		task.isFibonacciNo(14);
	}
}

Output

 Given 51 is not fibonacci number
 Given 144 is fibonacci number
 Given 987 is fibonacci number
 Given 14 is not fibonacci number
import Foundation;
// Swift 4 Program 
// Determine that if given number is Fibonacci Number
class FibonacciNumber
{
	func isFibonacciNo(_ n: Int)
	{
		//  5n²+4
		let a: Int = 5 * n * n + 4;
		//  5n²-4
		let b: Int = 5 * n * n - 4;
		let aSqrt: Int = Int((Double(a)).squareRoot());
		let bSqrt: Int = Int((Double(b)).squareRoot());
		if ((aSqrt * aSqrt) == a || (bSqrt * bSqrt) == b)
		{
			// When aSqrt or bSqrt is perfect square
			print("\n Given ", n ," is fibonacci number ", terminator: "");
		}
		else
		{
			print("\n Given ", n ," is not fibonacci number ", terminator: "");
		}
	}
}
func main()
{
	let task: FibonacciNumber = FibonacciNumber();
	// Test
	task.isFibonacciNo(51);
	task.isFibonacciNo(144);
	task.isFibonacciNo(987);
	task.isFibonacciNo(14);
}
main();

Output

 Given  51  is not fibonacci number
 Given  144  is fibonacci number
 Given  987  is fibonacci number
 Given  14  is not fibonacci number
// Kotlin Program 
// Determine that if given number is Fibonacci Number
class FibonacciNumber
{
	fun isFibonacciNo(n: Int): Unit
	{
		//  5n²+4
		val a: Int = 5 * n * n + 4;
		//  5n²-4
		val b: Int = 5 * n * n - 4;
		val aSqrt: Int = Math.sqrt(a.toDouble()).toInt();
		val bSqrt: Int = Math.sqrt(b.toDouble()).toInt();
		if ((aSqrt * aSqrt) == a || (bSqrt * bSqrt) == b)
		{
			// When aSqrt or bSqrt is perfect square
			print("\n Given " + n + " is fibonacci number ");
		}
		else
		{
			print("\n Given " + n + " is not fibonacci number ");
		}
	}
}
fun main(args: Array < String > ): Unit
{
	val task: FibonacciNumber = FibonacciNumber();
	// Test
	task.isFibonacciNo(51);
	task.isFibonacciNo(144);
	task.isFibonacciNo(987);
	task.isFibonacciNo(14);
}

Output

 Given 51 is not fibonacci number
 Given 144 is fibonacci number
 Given 987 is fibonacci number
 Given 14 is not fibonacci number

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