Check whether a number can be represented as difference of two squares

Given a number N, the task is to check if this number can be represented as the difference of two perfect squares or not.

Examples:

Input: N = 3 
Output: Yes 
Explanation:
2² – 1¹ = 3

Input: N = 10 
Output: No 

Approach: The idea is that all the numbers can be represented as the difference of two squares except the numbers which yield the remainder of 2 when divided by 4. 

Let’s visualize this by taking a few examples: 

N = 4 => 22 - 02
N = 6 => Can't be expressed as 6 % 4 = 2
N = 8 => 32 - 12
N = 10 => Can't be expressed as 10 % 4 = 2
N = 11 => 62 - 52
N = 12 => 42 - 22
and so on...

Therefore, the idea is to simply check the remainder for 2 when the given number is divided by 4.

Below is the implementation of the above approach: 

C++

// C++ program to check whether a number
// can be represented by the difference
// of two squares

#include <bits/stdc++.h>
using namespace std;

// Function to check whether a number
// can be represented by the difference
// of two squares
bool difSquare(int n)
{
    // Checking if n % 4 = 2 or not
    if (n % 4 != 2) {
        return true;
    }

    return false;
}

// Driver code
int main()
{

    int n = 45;
    if (difSquare(n)) {
        cout << "Yes\n";
    }
    else {
        cout << "No\n";
    }
    return 0;
}

Java

// Java program to check whether a number
// can be represented by the difference
// of two squares
import java.util.*;

class GFG{

// Function to check whether a number
// can be represented by the difference
// of two squares
static boolean difSquare(int n)
{

    // Checking if n % 4 = 2 or not
    if (n % 4 != 2)
    {
        return true;
    }
    return false;
}

// Driver code
public static void main(String[] args)
{
    int n = 45;

    if (difSquare(n))
    {
        System.out.print("Yes\n");
    }
    else
    {
        System.out.print("No\n");
    }
}
}

// This code is contributed by shivanisinghss2110

Python3

# Python3 program to check whether a number
# can be represented by the difference
# of two squares

# Function to check whether a number
# can be represented by the difference
# of two squares
def difSquare(n):

    # Checking if n % 4 = 2 or not
    if (n % 4 != 2):
        return True
    return False

# Driver code
if __name__ == '__main__':

    n = 45

    if (difSquare(n)):
        print("Yes")
    else:
        print("No")

# This code is contributed by mohit kumar 29

C#

// C# program to check whether a number
// can be represented by the difference
// of two squares
using System;
class GFG{

// Function to check whether a number
// can be represented by the difference
// of two squares
static bool difSquare(int n)
{

    // Checking if n % 4 = 2 or not
    if (n % 4 != 2)
    {
        return true;
    }
    return false;
}

// Driver code
public static void Main()
{
    int n = 45;

    if (difSquare(n))
    {
        Console.Write("Yes\n");
    }
    else
    {
        Console.Write("No\n");
    }
}
}

// This code is contributed by Nidhi_biet

Javascript

<script>

// Javascript program to check whether a number
// can be represented by the difference
// of two squares

// Function to check whether a number
// can be represented by the difference
// of two squares
function difSquare(n)
{

    // Checking if n % 4 = 2 or not
    if (n % 4 != 2)
    {
        return true;
    }
    return false;
}

// Driver code
var n = 45;

if (difSquare(n))
{
    document.write("Yes\n");
}
else
{
    document.write("No\n");
}

// This code is contributed by Rajput-Ji

</script>

Output:

Yes