## 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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