Timeline for Does the equation $x^2+x=a$ have an integer solution?

Current License: CC BY-SA 3.0

15 events

when toggle format	what		by	license	comment
Dec 25, 2017 at 13:21	vote	accept	Taras Banakh
Dec 25, 2017 at 1:08	comment	added	Daniel Loughran		I would not be surprised if the answer to your Question $2^n$ is no in general. Your problem looks very similar to the Grunwald–Wang theorem. As explained in the link, 16 is an 8th power modulo every odd prime $p$, but is clearly not an 8th power in $\mathbb{Z}$. I tried to use this to give a counter-example in the case $n=3$ and $a=16$, but alas it does not seem to work as the polynomial $(x^2 + x)^8 = 16$ has no root modulo $7$. However, something like this might still work.
Dec 24, 2017 at 15:40	history	edited	Taras Banakh	CC BY-SA 3.0	I edited the second question
Dec 24, 2017 at 14:01	history	edited	YCor	CC BY-SA 3.0	fixed English error in title, added link to def of Golomb space
Dec 24, 2017 at 12:56	answer	added	Will Sawin		timeline score: 9
Dec 24, 2017 at 12:22	comment	added	GH from MO		I added the analytic number theory tag, because the answers and history make it relevant.
Dec 24, 2017 at 12:22	history	edited	GH from MO		edited tags
Dec 24, 2017 at 12:00	history	edited	Joonas Ilmavirta	CC BY-SA 3.0	added 1 character in body
Dec 24, 2017 at 10:57	history	edited	GH from MO		edited tags
Dec 24, 2017 at 10:42	answer	added	GH from MO		timeline score: 18
Dec 24, 2017 at 10:41	answer	added	Wojowu		timeline score: 7
Dec 24, 2017 at 10:11	history	edited	Taras Banakh	CC BY-SA 3.0	deleted 95 characters in body
Dec 24, 2017 at 10:04	history	edited	Taras Banakh	CC BY-SA 3.0	Removed Fact 2 as I already know the answer
Dec 24, 2017 at 9:57	history	edited	Taras Banakh	CC BY-SA 3.0	Changed the title
Dec 24, 2017 at 8:51	history	asked	Taras Banakh	CC BY-SA 3.0