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

Difficulty Level : Hard
Last Updated : 13 Apr, 2021

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 => 4² - 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

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