Timeline for Is the number of solutions of $\phi(x)=n!$ bounded? If yes, what is its bound?
Current License: CC BY-SA 4.0
12 events
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| Jul 9, 2020 at 16:50 | answer | added | Emil Jeřábek | timeline score: 3 | |
| Jul 8, 2020 at 10:06 | comment | added | zeraoulia rafik | Thanks for the reference , I will check it | |
| Jul 8, 2020 at 10:04 | comment | added | Kasper Andersen | Actually Gupta proves that the number of solutions goes to infinity with $n$, see Hansraj Gupta, The American Mathematical Monthly, Vol. 57, No. 5 (May, 1950), pp. 326-329. | |
| Jul 8, 2020 at 9:34 | vote | accept | zeraoulia rafik | ||
| Jul 8, 2020 at 3:17 | answer | added | Gerhard Paseman | timeline score: 3 | |
| Jul 8, 2020 at 2:00 | comment | added | R. van Dobben de Bruyn | Quotes from A055506 and A055487 respectively: "All solutions to $\phi(x) = n!$ are in the interval $[n!,(n+1)!]$", and "According to Tattersall, in 1950 H. Gupta showed that $\phi(x) = n!$ is always solvable". The first gives a bound for fixed $n$, while the latter says that there exists a solution for any $n$. (I do not know arguments backing up either claim.) | |
| Jul 8, 2020 at 0:05 | review | Close votes | |||
| Jul 12, 2020 at 3:01 | |||||
| Jul 7, 2020 at 20:57 | history | edited | LSpice | CC BY-SA 4.0 |
Proofreading; link to paper
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| Jul 7, 2020 at 19:52 | answer | added | Max Alekseyev | timeline score: 8 | |
| Jul 7, 2020 at 11:28 | comment | added | Wojowu | For any fixed $n$, the number of solutions to $\phi(x)=n!$ is bounded, since $\phi(x)$ tends to infinity. However, this number is probably not bounded independently of $n$. | |
| Jul 7, 2020 at 9:59 | history | edited | zeraoulia rafik | CC BY-SA 4.0 |
edited body
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| Jul 7, 2020 at 9:36 | history | asked | zeraoulia rafik | CC BY-SA 4.0 |