# 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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