# Program to check if N is a Tetradecagonal Number

• Last Updated : 15 Jan, 2022

Given an integer N, the task is to check if N is a Tetradecagonal Number or not. If the number N is a Tetradecagonal Number then print “Yes” else print “No”.

Tetradecagonal Number is 14-sided polygon called Tetrakaidecagon or Tetradecagon and belongs to the figurative number. The nth tetradecagonal number dotted with some dots and create a series of the pattern. They have a common sharing corner point and dotted with their spaces to each other. The dots continue with nth nested loop.The first few Tetradecagonal Numbers are 1, 14, 39, 76, 125, 186, …

Examples:

Input: N = 14
Output: Yes
Explanation:

Input: N = 40
Output: No

Approach:

• The Kth term of the tetradecagonal number is given as
• As we have to check whether the given number can be expressed as a Tetradecagonal Number or not. This can be checked as:

=>
=>

• If the value of K calculated using the above formula is an integer, then N is a Tetradecagonal Number.
• Else N is not a Tetradecagonal Number.

Below is the implementation of the above approach:

## C++

 // C++ program for the above approach#include using namespace std; // Function to check if N is a// Tetradecagonal Numberbool istetradecagonal(int N){    float n        = (10 + sqrt(96 * N + 100))          / 24;     // Condition to check if the    // number is a tetradecagonal number    return (n - (int)n) == 0;} // Driver Codeint main(){    // Given Number    int N = 11;     // Function call    if (istetradecagonal(N)) {        cout << "Yes";    }    else {        cout << "No";    }    return 0;}

## Java

 // Java program for the above approachimport java.lang.Math; class GFG{     // Function to check if N is a// tetradecagonal numberpublic static boolean istetradecagonal(int N){    double n = (10 + Math.sqrt(96 * N +                               100)) / 24;         // Condition to check if the number    // is a tetradecagonal number    return (n - (int)n) == 0;} // Driver Code   public static void main(String[] args){             // Given number    int N = 11;         // Function call    if (istetradecagonal(N))    {        System.out.println("Yes");    }    else    {        System.out.println("No");    }}} // This code is contributed by divyeshrabadiya07

## Python3

 # Python3 program for the above approachimport math # Function to check if N is a# Tetradecagonal Numberdef istetradecagonal(N):         n = (10 + math.sqrt(96 * N + 100)) / 24         # Condition to check if the    # number is a tetradecagonal number    if (n - int(n)) == 0:        return True             return False # Driver Code # Given NumberN = 11 # Function callif (istetradecagonal(N)):    print("Yes")else:    print("No") # This code is contributed by shubhamsingh10

## C#

 // C# program for the above approachusing System; class GFG{     // Function to check if N is a// tetradecagonal numberpublic static bool istetradecagonal(int N){    double n = (10 + Math.Sqrt(96 * N +                               100)) / 24;             // Condition to check if the number    // is a tetradecagonal number    return (n - (int)n) == 0;}     // Driver Codestatic public void Main (){                 // Given number    int N = 11;             // Function call    if (istetradecagonal(N))    {        Console.Write("Yes");    }    else    {        Console.Write("No");    }}} // This code is contributed by shubhamsingh10

## Javascript

 

Output:

No

Time Complexity: O(1)

Auxiliary Space: O(1)

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