Timeline for A hard diophantine equation: $m!+27=n^3$

Current License: CC BY-SA 4.0

12 events

when toggle format	what		by	license	comment
Mar 3, 2023 at 10:45	history	edited	Martin Sleziak	CC BY-SA 4.0	replaced the dead link
May 13, 2012 at 17:19	vote	accept	Roberto Bosch Cabrera
May 10, 2012 at 1:15	history	edited	GH from MO	CC BY-SA 3.0	deleted 4 characters in body
May 10, 2012 at 1:03	history	edited	GH from MO	CC BY-SA 3.0	added 430 characters in body
May 9, 2012 at 20:10	history	edited	GH from MO	CC BY-SA 3.0	added 653 characters in body
May 8, 2012 at 23:24	comment	added	Roberto Bosch Cabrera		@GH: Thank you for your new Edit proving that $m<10^{12}$.
May 8, 2012 at 21:10	history	edited	GH from MO	CC BY-SA 3.0	added 139 characters in body
May 8, 2012 at 18:58	history	edited	GH from MO	CC BY-SA 3.0	added 316 characters in body
May 8, 2012 at 16:06	comment	added	GH from MO		It seems that Erdős's paper contains everything needed for a solution. Namely, we are dealing with (8), where $p=3$ and $y=3$. Hence (10) needs to be adjusted slightly: $B_2\leq 27 T(n,6)$. From here it should be easy to finish the solution. At the heart of the argument is (Va), which is a clever explicit substitute of Dirichlet's theorem.
May 8, 2012 at 15:14	comment	added	Roberto Bosch Cabrera		This problem arise (it is the hard part) when we try to solve the equation: $x!+y!+3=Z^3$ which was proposed as $J198$ in Mathematical Reflections. I think that the solution can be found in (1) renyi.hu/~p_erdos/1937-09.pdf (2) ams.org/journals/tran/2006-358-04/S0002-9947-05-03780-3/… but I'm not sure. I'm trying to find an "elementary" solution.
May 8, 2012 at 14:51	comment	added	Roberto Bosch Cabrera		Thank you so much GH, now it is interesting find an upper bound for $m$ such that we can begin a computer search.
May 8, 2012 at 5:18	history	answered	GH from MO	CC BY-SA 3.0