Comprobar si un número se puede representar como diferencia de dos cuadrados

Dado un número N , la tarea es verificar si este número se puede representar como la diferencia de dos cuadrados perfectos o no.

Ejemplos: 

Entrada: N = 3 
Salida: Sí 
Explicación: 
2 ² – 1 ¹ = 3

Entrada: N = 10 
Salida: No 
 

Enfoque: La idea es que todos los números se pueden representar como la diferencia de dos cuadrados, excepto los números que dan el resto de 2 cuando se dividen por 4. 

Visualicemos esto tomando algunos ejemplos: 

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...

Por lo tanto, la idea es simplemente comprobar el resto de 2 cuando el número dado se divide por 4.

A continuación se muestra la implementación del enfoque anterior: 

// 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 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 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# 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

<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>

Yes