# Smallest number whose sum of digits is square of N

Given an integer N, the task is to find the smallest number whose sum of digits is N2.

Examples:

Input: N = 4
Output: 79
24 = 16
sum of digits of 79 = 76

Input: N = 6
Output: 9999
210 = 1024 which has 4 digits

Approach: The idea is to find the general term for the smallest number whose sum of digits is square of N. That is

```// First Few terms
First Term = 1 // N = 1
Second Term = 4 // N = 2
Third Term = 9 // N = 3
Fourth Term = 79 // N = 4
.
.
Nth Term:```

```*** QuickLaTeX cannot compile formula:

*** Error message:
Error: Nothing to show, formula is empty
```

` <sup>(n^2 \% 9 + 1) * 10 ^ {\lfloor n^2/9 \rfloor} - 1 </sup>`

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the above approach`   `#include ` `using` `namespace` `std;`   `// Function to return smallest` `// number whose sum of digits is n^2` `int` `smallestNum(``int` `n)` `{` `    ``return` `(n * n % 9 + 1) * ``pow``(10, n * n / 9) - 1;` `}`   `// Driver Code` `int` `main()` `{` `    ``int` `n = 4;` `    ``cout << smallestNum(n);`   `    ``return` `0;` `}`

## Java

 `// Java implementation of the above approach` `import` `java.util.*;`   `class` `GFG{`   `// Function to return smallest` `// number whose sum of digits is n^2` `static` `int` `smallestNum(``int` `n)` `{` `    ``return` `(``int``)((n * n % ``9` `+ ``1``) * ` `         ``Math.pow(``10``, n * n / ``9``) - ``1``);` `}`   `// Driver Code` `public` `static` `void` `main(String[] args)` `{` `    ``int` `n = ``4``;` `    `  `    ``System.out.print(smallestNum(n));` `}` `}`   `// This code is contributed by Rajput-Ji`

## Python 3

 `# Python implementation of the above approach `   `# Function to return smallest ` `# number whose sum of digits is n^2 ` `def` `smallestNum(n):`   `    ``return` `((n ``*` `n ``%` `9` `+` `1``)  ``*` `          ``pow``(``10``, ``int``(n ``*` `n ``/` `9``)) ``-` `1``) `   `# Driver Code`   `# Given N` `N ``=` `4`   `print``(smallestNum(N))`   `# This code is contributed by Vishal Maurya.`

## C#

 `// C# implementation of the above approach` `using` `System;`   `class` `GFG{`   `// Function to return smallest` `// number whose sum of digits is n^2` `static` `int` `smallestNum(``int` `n)` `{` `    ``return` `(``int``)((n * n % 9 + 1) * ` `         ``Math.Pow(10, n * n / 9) - 1);` `}`   `// Driver Code` `public` `static` `void` `Main(String[] args)` `{` `    ``int` `n = 4;` `    `  `    ``Console.Write(smallestNum(n));` `}` `}`   `// This code is contributed by Rajput-Ji`

## Javascript

 ``

Output

```10
79```

Time complexity: O(log10n2)  for given n, as pow function is being used
Auxiliary space: O(1)

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