# Smallest N digit number which is a perfect fourth power

Given an integer N, the task is to find the smallest N-digit number which is a perfect fourth power.

Examples:

Input: N = 2
Output: 16
Only valid numbers are 24 = 16
and 34 = 81 but 16 is the minimum.

Input: N = 3
Output: 256
44 = 256

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

Approach: It can be observed that for the values of N = 1, 2, 3, …, the series will go on like 1, 16, 256, 1296, 10000, 104976, 1048576, … whose Nth term will be pow(ceil( (pow(pow(10, (n – 1)), 1 / 4) ) ), 4).

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach ` `#include ` ` `  `using` `namespace` `std; ` ` `  `// Function to return the smallest n-digit ` `// number which is a perfect fourth power ` `int` `cal(``int` `n) ` `{ ` `    ``double` `res = ``pow``(``ceil``((``pow``(``pow``(10,  ` `                          ``(n - 1)), 1 / 4) )), 4); ` `    ``return` `(``int``)res; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `n = 1; ` `    ``cout << (cal(n)); ` `} ` ` `  `// This code is contributed by Mohit Kumar `

## Java

 `// Java implementation of the approach ` `class` `GFG ` `{ ` ` `  `// Function to return the smallest n-digit ` `// number which is a perfect fourth power ` `static` `int` `cal(``int` `n) ` `{ ` `    ``double` `res = Math.pow(Math.ceil(( ` `                 ``Math.pow(Math.pow(``10``,  ` `                ``(n - ``1``)), ``1` `/ ``4``) )), ``4``); ` `    ``return` `(``int``)res; ` `} ` ` `  `// Driver code ` `public` `static` `void` `main(String[] args) ` `{ ` `    ``int` `n = ``1``; ` `    ``System.out.println(cal(n)); ` `} ` `} ` ` `  `// This code is contributed by CodeMech `

## Python3

 `# Python3 implementation of the approach ` `from` `math ``import` `*` ` `  `# Function to return the smallest n-digit  ` `# number which is a perfect fourth power ` `def` `cal(n): ` `    ``res ``=` `pow``(ceil( (``pow``(``pow``(``10``, (n ``-` `1``)), ``1` `/` `4``) ) ), ``4``) ` `    ``return` `int``(res) ` ` `  `# Driver code ` `n ``=` `1` `print``(cal(n)) `

## C#

 `// C# implementation of the approach ` `using` `System; ` ` `  `class` `GFG ` `{ ` ` `  `// Function to return the smallest n-digit ` `// number which is a perfect fourth power ` `static` `int` `cal(``int` `n) ` `{ ` `    ``double` `res = Math.Pow(Math.Ceiling(( ` `                 ``Math.Pow(Math.Pow(10,  ` `                 ``(n - 1)), 1 / 4) )), 4); ` `    ``return` `(``int``)res; ` `} ` ` `  `// Driver code ` `public` `static` `void` `Main() ` `{ ` `    ``int` `n = 1; ` `    ``Console.Write(cal(n)); ` `} ` `} ` ` `  `// This code is contributed  ` `// by Akanksha_Rai `

Output:

```1
```

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