Timeline for Does the equation in positive integers $(n,y)\,\prod_{k=1}^n(p_k^2-1)=y^2\,$ only have the solution $(3,24)$?
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 3, 2021 at 10:54 | comment | added | Sylvain JULIEN | This may have something to do with Mihailescu theorem (former Catalan conjecture), if we manage to prove $p_{k}^{2}-1$ has to be a perfect power as well as a divisor of $y$ for some $k$. | |
| Dec 27, 2020 at 17:51 | comment | added | JoshuaZ | To expand on @FedorPetrov 's comment. the density of Germain primes en.wikipedia.org/wiki/Safe_and_Sophie_Germain_primes strongly suggest that for any such product which is sufficiently large, one will have at least prime p where $p^2 -1$ is divisible by a very big prime tha has not shown up anywhere else in the product. | |
| Dec 27, 2020 at 14:42 | answer | added | მამუკა ჯიბლაძე | timeline score: 3 | |
| Dec 27, 2020 at 12:39 | comment | added | Fedor Petrov | Probably no, but looks hopeless. There should be many primes for which $2p+1$ is prime and $4p-1$ is too large. | |
| Dec 27, 2020 at 11:26 | history | asked | Augusto Santi | CC BY-SA 4.0 |