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Jul 8, 2022 at 20:13 comment added Harry Wilson Ten years on from Asaf's comment I would like to mention that I have never felt loneliness. Nor guilt or disgust, for that matter. But I'm not dead yet, so this of course doesn't actually disprove anything.
Feb 2, 2019 at 13:14 comment added PatrickT The conjecture was proved in the special case where the distance is long. See en.wikipedia.org/wiki/…
Oct 31, 2016 at 6:28 history edited Martin Sleziak CC BY-SA 3.0
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Oct 5, 2015 at 6:45 comment added pageman Here's a post by Terence Tao on this conjecture: terrytao.wordpress.com/2015/05/13/…
Jul 2, 2012 at 2:14 comment added Andrew Dudzik This is open for $k\geq 7$. The proof for $k=6$ was done by Barajas and Serra using elaborate computer-assisted casework, and many simplifications that rely on the fact that $6+1$ is prime. It is worth noting that when the ratio of two speeds is irrational, the problem is made easier by density arguments, so the essentially hardest case is when all the speeds are integers. Therefore this is a combinatorial number theory question disguised as basic calculus.
Jun 22, 2012 at 20:59 comment added Asaf Karagila Observe that the human condition implies that everyone gets lonely at some time. In particular the runners get lonely.
Jun 22, 2012 at 18:59 comment added Gerhard Paseman Also, I suspect this is equivalent to the lonely starting post conjecture, which is the conjecture above except that one of the runners has speed 0 and the statement is that he/she gets lonely. Gerhard "Ask Me About Going Slow" Paseman, 2012.06.22
Jun 22, 2012 at 18:43 comment added Gerhard Paseman For k=1, this does not happen for very long. Gerhard "As( Me About System Design" Paseman, 2012.06.22
Jun 22, 2012 at 18:24 history answered Timothy Chow CC BY-SA 3.0