Timeline for Does this equation have more than one integer solution?

9 events

when toggle format	what		by	license	comment
Feb 23, 2020 at 19:42	answer	added	Mike Bennett		timeline score: 15
Feb 19, 2020 at 5:42	comment	added	user44191		Something that may help: $n + 1 = \frac{2^y - 2^x}{2^y - 3^x}$, so there is such an $n$ iff $2^y - 3^x \| 2^y - 2^x$. The denominator is odd, so there is such an $n$ iff $2^y - 3^x \| 2^{y - x} - 1$. Notice that this implies that $2^{y - 1} < 3^x < 2^y$, so for each $y$, there's only one $x$ to check.
Feb 17, 2020 at 15:41	comment	added	Xarles		It is not a solution because of the last inequality, but $x=2$ and $y=3$, so $n=-5$, it is an integer solution of the equation (which I am reluctant to say is Diophantine).
Feb 17, 2020 at 14:09	history	edited	Lee		edited tags
S Feb 16, 2020 at 20:16	history	suggested	RobPratt	CC BY-SA 4.0	Corrected title and added math mode
Feb 16, 2020 at 19:20	review	Close votes
Feb 23, 2020 at 20:10
Feb 16, 2020 at 18:02	review	Suggested edits
S Feb 16, 2020 at 20:16
Feb 16, 2020 at 17:25	review	First posts
Feb 16, 2020 at 19:28
Feb 16, 2020 at 17:22	history	asked	Lee	CC BY-SA 4.0