Lonely runner conjecture
Number-theoretic conjecture that states that 𝑘 people running around a circular track with distinct speeds will each be, at some point, separated by ¹⁄ₖ from every other runner
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Lonely runner conjecture
Number-theoretic conjecture that states that 𝑘 people running around a circular track with distinct speeds will each be, at some point, separated by ¹⁄ₖ from every other runner
In number theory, specifically the study of Diophantine approximation, the lonely runner conjecture is a conjecture about the long-term behavior of runners on a circular track. It states that n {\displaystyle n} runners on a track of unit length, with constant speeds all distinct from one another, will each be lonely at some time—at least 1 / n {\displaystyle 1/n} units away from all others.
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From Wikipedia
In number theory, specifically the study of Diophantine approximation, the lonely runner conjecture is a conjecture about the long-term behavior of runners on a circular track. It states that n {\displaystyle n} runners on a track of unit length, with constant speeds all distinct from one another, will each be lonely at some time—at least 1 / n {\displaystyle 1/n} units away from all others. The conjecture was first posed in 1967 by German mathematician Jörg Wills, in purely number-theoretic terms, and independently as a view-obstruction problem in 1974 by Thomas W. Cusick; its illustrative and now-popular formulation dates to 1998. The conjecture is known to be true for 13 {\displaystyle 13} runners or fewer, but the general case remains unsolved. Implications of the conjecture include solutions to view-obstruction problems and bounds on properties, related to chromatic numbers, of certain graphs.
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