## Solution to: Elegant Equation

Make a long division:

```    4/4.....\......
```

Calculate the first digit of the result:

```    4/4.....\1.....
4
--
0
```

Now we also know that the next digit of the dividend is a 1:

```    4/41....\1.....
4
--
0
```

Then we can calculate the next digit of the result:

```    4/41....\10....
4
--
01
0
--
1
```

Therefore, the next digit of the dividend is also a 0:

```    4/410...\10....
4
--
01
0
--
1
```

This process of calculating the next digit of the result and adding it to the dividend must be repeated until the remainder is 0 and the last digit of the result is a 4:

```    4/410256\102564
4
--
01
0
--
10
8
--
22
20
--
25
24
--
16
16
--
0
```

Conclusion: the number we were looking for is 10256.

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