# 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

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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 ` `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 `

Output:

```Yes
```

Don’t stop now and take your learning to the next level. Learn all the important concepts of Data Structures and Algorithms with the help of the most trusted course: DSA Self Paced. Become industry ready at a student-friendly price.

My Personal Notes arrow_drop_up If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.

Article Tags :
Practice Tags :

6

Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.