INMO 2015 Problem 2

[Writika Sarkar]

Problem: Let \(n\) be natural number greater than \(1\). Consider the infinite decimal representation of \(\frac{1}{n}\). For example, the infinite decimal representation of \(\frac{1}{2}\) is \(0.4\overline{9}\) and not \(0.5\). Determine the non-repeating part of the infinite decimal representation of \(\frac{1}{n}\).

Here is the link to my solution, which is not matching with the official solution. Could someone kindly check this and tell me if this proof is correct and rigorous enough?
Thanks.

[Writika Sarkar]

Please check this link actually. The write-up of the previous one was pretty complicated.

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