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Check if N can be represented as sum of squares of two consecutive integers
• Last Updated : 11 Jun, 2020

Given an integer N, the task is to check whether N can be represented as a sum of squares of two consecutive integers or not.

Examples:

Input: N = 5
Output: Yes
Explanation:
The integer 5 = 12 + 22 where 1 and 2 are consecutive numbers.

Input: 13
Output: Yes
Explanation:
13 = 22 + 32

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

Approach: This equation can be represented as:

=> => => Finally, check the value of computed using this formula is an integer, which means that N can be represented as the sum of squares 2 consecutive integers

Below is the implementation of the above approach:

## C++

 // C++ implementation to check that  // a number is sum of squares of 2  // consecutive numbers or not     #include  using namespace std;     // Function to check that the  // a number is sum of squares of 2  // consecutive numbers or not  bool isSumSquare(int N)  {      float n          = (2 + sqrt(8 * N - 4))            / 2;         // Condition to check if the      // a number is sum of squares of 2      // consecutive numbers or not      return (n - (int)n) == 0;  }     // Driver Code  int main()  {      int i = 13;         // Function call      if (isSumSquare(i)) {          cout << "Yes";      }      else {          cout << "No";      }      return 0;  }

## Java

 // Java implementation to check that   // a number is sum of squares of 2   // consecutive numbers or not   import java.lang.Math;     class GFG{         // Function to check that the   // a number is sum of squares of 2   // consecutive numbers or not   public static boolean isSumSquare(int N)   {       double n = (2 + Math.sqrt(8 * N - 4)) / 2;              // Condition to check if the       // a number is sum of squares of 2       // consecutive numbers or not       return(n - (int)n) == 0;   }      // Driver code   public static void main(String[] args)  {      int i = 13;          // Function call       if (isSumSquare(i))      {           System.out.println("Yes");      }       else     {           System.out.println("No");      }   }  }     // This code is contributed by divyeshrabadiya07

## Python3

 # Python3 implementation to check that   # a number is sum of squares of 2   # consecutive numbers or not   import math     # Function to check that the a  # number is sum of squares of 2   # consecutive numbers or not   def isSumSquare(N):         n = (2 + math.sqrt(8 * N - 4)) / 2            # Condition to check if the a       # number is sum of squares of      # 2 consecutive numbers or not      return (n - int(n)) == 0    # Driver code   if __name__=='__main__':             i = 13            # Function call      if isSumSquare(i):          print('Yes')      else :          print('No')     # This code is contributed by rutvik_56

## C#

 // C# implementation to check that   // a number is sum of squares of 2   // consecutive numbers or not   using System;  class GFG{         // Function to check that the   // a number is sum of squares of 2   // consecutive numbers or not   public static bool isSumSquare(int N)   {       double n = (2 + Math.Sqrt(8 * N - 4)) / 2;              // Condition to check if the       // a number is sum of squares of 2       // consecutive numbers or not       return(n - (int)n) == 0;   }      // Driver code   public static void Main(String[] args)  {      int i = 13;          // Function call       if (isSumSquare(i))      {           Console.WriteLine("Yes");      }       else     {           Console.WriteLine("No");      }   }  }     // This code is contributed by sapnasingh4991

Output:

Yes


Note: In order to print the integers, we can easily solve the above equation to get the roots.

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