prithivMLmods/Coder-Stat

1<h1>Dudeney Number</h1>2　3<p>4  A Dudeney number is a positive integer for which the sum of its decimal digits is equal to the cube root of the number. For example, $512$ is a Dudeney number because it is the cube of $8$, which is the sum of its decimal digits ($5 + 1 + 2$).5</p>6<p>7  In this problem, we think of a type similar to Dudeney numbers and try to enumerate them.8</p>9<p>10  Given a non-negative integer $a$, an integer $n$ greater than or equal to 2 and an upper limit $m$, make a program to enumerate all $x$’s such that the sum of its decimal digits $y$ satisfies the relation $x = (y + a)^n$, and $x \leq m$.11</p>12 13<h2>Input</h2>14<p>15The input is given in the following format.16</p>17<pre>18$a$ $n$ $m$19</pre>20 21<p>22  The input line provides three integers: $a$ ($0 \leq a \leq 50$), $n$ ($2 \leq n \leq 10$) and the upper limit $m$ ($1000 \leq m \leq 10^8$).23</p>24 25<h2>Output</h2>26<p>27  Output the number of integers that meet the above criteria.28</p>29 30<h2>Sample Input 1</h2>31<pre>3216 2 100033</pre>34 35<h2>Sample Output 1<h2>36<pre>37238</pre>39<p>40  Two:  $400 = (4 + 0 + 0 + 16)^2$ and $841 = (8 + 4 + 1 + 16)^2$41</p>42 43 44<h2>Sample Input 2</h2>45<pre>460 3 500047</pre>48 49<h2>Sample Output 2</h2>50<pre>51352</pre>53<p>54  Three: $1=1^3$, $512 = (5 + 1 + 2)^3$ and $4913 = (4 + 9 + 1 + 3)^3$.55</p>56 57<h2>Sample Input 3</h2>58<pre>592 3 10000060</pre>61 62<h2>Sample Output 3</h2>63<pre>64065</pre>66<p>67  There is no such number $x$ in the range below $100,000$ such that its sum of decimal digits $y$ satisfies the relation $(y+2)^3 = x$.68</p>69 70