Timeline for A number theory problem related to graph spectra?

6 events

when toggle format	what		by	license	comment
May 11, 2016 at 16:13	answer	added	Gerhard Paseman		timeline score: 2
May 11, 2016 at 15:59	comment	added	Geoff Robinson		Since $p^{2} \equiv 1$ (mod $8$) for odd $p$, we can't have $2^{n} = p^{2}+1$, and more generally, $2^{n}= p^{k}+1$ gives that $k$ must be odd. Of course any Mersenne prime $p$ works with $k = 1$, so suppose $k > 1.$ However, it is easy to check that $\frac{p{k}+1}{p+1}$ is then odd, a contradiction. So the only solutions (to the second question) are when $p$ is a Mersenne prime and $k=1$. There are no solutions to the first question ( Obsolete by Douglas Zare's link to a more general answer).
May 11, 2016 at 15:46	comment	added	Douglas Zare		en.wikipedia.org/wiki/Catalan%27s_conjecture
May 11, 2016 at 15:43	comment	added	Douglas Zare		What is the connection to graph spectra?
May 11, 2016 at 15:42	review	First posts
May 11, 2016 at 17:38
May 11, 2016 at 15:41	history	asked	user91523	CC BY-SA 3.0