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 => 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++

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// 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;
}

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Java

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// 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

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Python3

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# 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

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C#

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// 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

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Output:

Yes

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