Timeline for Can one show combinatorially how $\operatorname{lcm}(1, \dotsc, n)$ grows?

6 events

when toggle format	what		by	license	comment
May 21, 2020 at 10:11	comment	added	GH from MO		This argument assumes that $n$ is odd, and it gives $M(n-1)>2^{n-1}$. It would be cleaner to write the proof for $n$ even, with $P(x)=x^{n/2}(1-x)^{n/2}$, and obtain $M(n)>2^n$. For $n$ odd, it follows that $M(n)>M(n-1)>2^{n-1}$. So we have $M(n)>2^{n-1}$ in all cases.
May 21, 2020 at 10:06	history	edited	GH from MO	CC BY-SA 4.0	fixed two typos
May 21, 2020 at 4:40	comment	added	Mark Lewko		Gerhard: Yes, that seems right. I've added Schnirelmann in the citation and corrected the 4 to a 2.
May 21, 2020 at 4:39	history	edited	Mark Lewko	CC BY-SA 4.0	added 19 characters in body
May 21, 2020 at 4:29	comment	added	Gerhard Paseman		This is much like the argument I attribute to Nair. In section 9 of his article Diamond says Nair rediscovered it, and gives Gelfond and Schnirelmann as a reference. Also, the 4 should be more like 2. Gerhard "Deflation These Days, You Know?" Paseman, 2020.05.20.
May 21, 2020 at 4:20	history	answered	Mark Lewko	CC BY-SA 4.0