Timeline for Is $\Bigl\{ n \sum_{k=2}^{n-1} \frac{1}{k}\Bigr\}$ unique $\forall n \in \Bbb{N}, n>1$
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 15, 2020 at 15:37 | vote | accept | swami | ||
| Nov 12, 2020 at 21:26 | answer | added | Lucia | timeline score: 13 | |
| Nov 12, 2020 at 18:19 | answer | added | Sylvain JULIEN | timeline score: 2 | |
| Nov 12, 2020 at 14:12 | answer | added | Carlo Beenakker | timeline score: 9 | |
| Nov 12, 2020 at 12:17 | comment | added | Carlo Beenakker | so the question is equivalent to asking whether $nH_{n}-mH_{m}$ can be an integer for $n\neq m$; note that it is known that the difference $H_{n}-H_{m}$ of two different harmonic numbers cannot be an integer, perhaps the proof can be applied to this question as well | |
| Nov 12, 2020 at 12:16 | comment | added | Sylvain JULIEN | Perhaps we could first show this holds for all integers sharing the same radical. Given an integer $n$ the smallest integer $n'$ greater than $n$ with the same radical is $2n$, but then from Bertrand's postulate a new prime appears among the $k$ one sums over, hence giving rise to a new denominator for the rational number the considered fractional part is equal to. | |
| Nov 12, 2020 at 11:56 | comment | added | Carlo Beenakker | true up to $n=10^4$ | |
| Nov 12, 2020 at 11:50 | history | asked | swami | CC BY-SA 4.0 |