Check if N can be represented as sum of squares of two consecutive integers
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
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 <bits/stdc++.h> 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; } |
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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 |
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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 |
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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 |
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Output:
Yes
Note: In order to print the integers, we can easily solve the above equation to get the roots.
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