Timeline for Primes from a Dirichlet sequence and an irrational number
Current License: CC BY-SA 3.0
7 events
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| Jun 28, 2014 at 23:50 | history | edited | José Hdz. Stgo. | CC BY-SA 3.0 |
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| Jun 28, 2014 at 8:54 | history | edited | José Hdz. Stgo. | CC BY-SA 3.0 |
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| Jun 28, 2014 at 8:53 | comment | added | José Hdz. Stgo. | Apply reductio ad absurdum. Suppose that the number $\alpha$ is a rational number. We may even assume that $\alpha$ has a periodic decimal representation and that its period starts right after the decimal comma. Let $s$ denote the period length of $\alpha$. It is not difficult to establish, that for every $k\in \mathbb{N}$, the sequence $\{a_{i}\}_{i \in \mathbb{N}}$ has no more that $s$ terms of $k$ digits. Hence, $\sum_{i=1}^{\infty} \frac{1}{a_{i}} \leq \sum_{i=1}^{\infty} \frac{s}{10^{i-1}}$, which contradicts the divergence of the series $\sum_{i=1}^{\infty}\frac{1}{a_{i}}$... | |
| Jun 28, 2014 at 8:19 | comment | added | shadow10 | Hi, could you post the solution? I couldn't find it on the web. Thanks a lot. | |
| Jun 28, 2014 at 8:18 | history | edited | José Hdz. Stgo. | CC BY-SA 3.0 |
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| Jun 28, 2014 at 8:10 | history | edited | José Hdz. Stgo. | CC BY-SA 3.0 |
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| Jun 28, 2014 at 8:03 | history | answered | José Hdz. Stgo. | CC BY-SA 3.0 |