Critic Ivor Smallbrain is watching the classic film 11. \(\overline{9}\) Angry Men. But he is bored, and starts wondering idly exactly which rational numbers \(\frac{1}{n}\) have decimal expressions with period equal to 1 . Having done the previous question during the advertisments before the film, he notices that the period is 1 if the denominator \(n\) is \(2^{a} 5^{b}\). But he also notices some other values of \(n\) for which the period is 1 , such as \(n=3\).

Can you help Ivor and find all the values of \(n\) for which \(\frac{1}{n}\) has period 1 ?