# Program to check if N is a Icositetragonal number

Given an integer **N**, the task is to check if it is a icositetragonal number or not.

icositetragonal number:

s a class of figurate number. It has a 24-sided polygon called Icositetragon. The N-th Icositetragonal number countâ€™s the number of dots and all others dots are surrounding with a common sharing corner and make a pattern

The first few icositetragonal numbers are 1, 24, 69, 136, 225, 336, …

**Examples:**

Input:N = 24Output:YesExplanation:

Second icositetragonal number is 24.Input:N = 30Output:No

**Approach:**

- The K
^{th}term of the icositetragonal number is given as

- As we have to check that the given number can be expressed as a icositetragonal number or not. This can be checked as follows –

=>

=>

- Finally, check the value of computed using this formulae is an integer, which means that N is a icositetragonal number.

Below is the implementation of the above approach:

## C++

`// C++ implementation to check that` `// a number is icositetragonal number or not` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to check that the` `// number is a icositetragonal number` `bool` `isicositetragonal(` `int` `N)` `{` ` ` `float` `n` ` ` `= (10 + ` `sqrt` `(44 * N + 100))` ` ` `/ 22;` ` ` `// Condition to check if the` ` ` `// number is a icositetragonal number` ` ` `return` `(n - (` `int` `)n) == 0;` `}` `// Driver Code` `int` `main()` `{` ` ` `int` `i = 24;` ` ` `// Function call` ` ` `if` `(isicositetragonal(i)) {` ` ` `cout << ` `"Yes"` `;` ` ` `}` ` ` `else` `{` ` ` `cout << ` `"No"` `;` ` ` `}` ` ` `return` `0;` `}` |

## Java

`// Java implementation to check that` `// a number is icositetragonal number or not` `class` `GFG{` `// Function to check that the` `// number is a icositetragonal number` `static` `boolean` `isicositetragonal(` `int` `N)` `{` ` ` `float` `n = (` `float` `)((` `10` `+ Math.sqrt(` `44` `* N +` ` ` `100` `)) / ` `22` `);` ` ` `// Condition to check if the` ` ` `// number is a icositetragonal number` ` ` `return` `(n - (` `int` `)n) == ` `0` `;` `}` `// Driver Code` `public` `static` `void` `main(String[] args)` `{` ` ` `int` `i = ` `24` `;` ` ` `// Function call` ` ` `if` `(isicositetragonal(i))` ` ` `{` ` ` `System.out.print(` `"Yes"` `);` ` ` `}` ` ` `else` ` ` `{` ` ` `System.out.print(` `"No"` `);` ` ` `}` `}` `}` `// This code is contributed by 29AjayKumar` |

## Python3

`# Python3 implementation to check that` `# a number is icositetragonal number` `# or not` `import` `math` `# Function to check that the number` `# is a icositetragonal number` `def` `isicositetragonal(N):` ` ` `n ` `=` `(` `10` `+` `math.sqrt(` `44` `*` `N ` `+` `100` `)) ` `/` `22` ` ` `# Condition to check if the number` ` ` `# is a icositetragonal number` ` ` `return` `(n ` `-` `int` `(n)) ` `=` `=` `0` `# Driver Code` `i ` `=` `24` `# Function call` `if` `(isicositetragonal(i)):` ` ` `print` `(` `"Yes"` `)` `else` `:` ` ` `print` `(` `"No"` `)` `# This code is contributed by divyamohan123` |

## C#

`// C# implementation to check that` `// a number is icositetragonal number or not` `using` `System;` `class` `GFG{` `// Function to check that the` `// number is a icositetragonal number` `static` `bool` `isicositetragonal(` `int` `N)` `{` ` ` `float` `n = (` `float` `)((10 + Math.Sqrt(44 * N +` ` ` `100)) / 22);` ` ` `// Condition to check if the` ` ` `// number is a icositetragonal number` ` ` `return` `(n - (` `int` `)n) == 0;` `}` `// Driver Code` `public` `static` `void` `Main()` `{` ` ` `int` `i = 24;` ` ` `// Function call` ` ` `if` `(isicositetragonal(i))` ` ` `{` ` ` `Console.Write(` `"Yes"` `);` ` ` `}` ` ` `else` ` ` `{` ` ` `Console.Write(` `"No"` `);` ` ` `}` `}` `}` `// This code is contributed by Akanksha_Rai` |

## Javascript

`<script>` `// JavaScript implementation to check that` `// a number is icositetragonal number or not` `// Function to check that the` `// number is a icositetragonal number` `function` `isicositetragonal(N)` `{` ` ` `var` `n = (10 + Math.sqrt(44 * N + 100))` ` ` `/ 22;` ` ` `// Condition to check if the` ` ` `// number is a icositetragonal number` ` ` `return` `(n - parseInt(n)) == 0;` `}` `// Driver Code` `var` `i = 24;` `// Function call` `if` `(isicositetragonal(i)) {` ` ` `document.write(` `"Yes"` `);` `}` `else` `{` ` ` `document.write(` `"No"` `);` `}` ` ` `</script>` |

**Output:**

Yes

**Time Complexity: **O(1)

**Auxiliary Space: **O(1)

Attention reader! Don’t stop learning now. Get hold of all the important mathematical concepts for competitive programming with the **Essential Maths for CP Course** at a student-friendly price. To complete your preparation from learning a language to DS Algo and many more, please refer **Complete Interview Preparation Course****.**