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 = 3Input: 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; } |
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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 |
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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 |
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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 |
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Output:
Yes
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