The Lonely Runner Conjecture of Wills and Cusick states that if $k+1$ runners start running at distinct constant speeds around a unit-length circular track, then for each runner there is a time when he/she is at least $1/(k+1)$ away from all other runners. Rosenfeld recently obtained a computer-assisted proof of the conjecture for $8$ runners. By refining his approach with a sieve, we obtain proofs (also computer-assisted) for $9$ and $10$ runners.

翻译：威尔斯和库西克提出的“孤独跑者猜想”指出，如果 $k+1$ 名跑者以不同的恒定速度在单位长度的圆形跑道上起跑，那么对于每一名跑者，存在一个时刻，他/她与所有其他跑者的距离至少为 $1/(k+1)$。罗森菲尔德最近通过计算机辅助方法证明了该猜想对于 $8$ 名跑者成立。通过采用筛法改进他的方法，我们获得了针对 $9$ 名和 $10$ 名跑者的证明（同样借助计算机辅助）。