The Lonely Runner Conjecture for Nine and Ten Runners
Prior state unknown→proved
Settles 9 and 10 runners only; the general conjecture remains open.
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number-theory / Diophantine approximation
The Lonely Runner Conjecture for Nine and Ten Runners
The Lonely Runner Conjecture of Wills and Cusick states that among $k+1$ runners at distinct constant speeds on a unit circle, each runner is at some time at distance at least $1/(k+1)$ from all others. Following Rosenfeld's computer-assisted proof for 8 runners, the paper refines his approach with a sieve and proves the cases of 9 and 10 runners.
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The Lonely Runner Conjecture of Wills and Cusick states that among $k+1$ runners at distinct constant speeds on a unit circle, each runner is at some time at distance at least $1/(k+1)$ from all others. Following Rosenfeld's computer-assisted proof for 8 runners, the paper refines his approach with a sieve and proves the cases of 9 and 10 runners.
Settles 9 and 10 runners only; the general conjecture remains open.
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