Irreducible number

Number theory
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Riemann
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Location: Melbourne, Australia

Irreducible number

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Denote by $\bar{\alpha}=0.\alpha \alpha \alpha \dots $. Find all $\alpha>0$ such that

$$\frac{1}{\alpha} = 0.\bar{a}$$
$\displaystyle \sum_{n=1}^{\infty}\frac{1}{n^s}= \prod_{p \; \text{prime}}\frac{1}{1-p^{-s}}$
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