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There are Abhyankar’s conjectures in Galois theory, namely Abhyankar’s Conjecture for affine curves, Abhyankar’s Inertia Conjecture and Abhyankar’s Affine Arithmetical Conjecture. All three conjectures are about Galois theory in positive characteristic, related to algebraic and etale fundamental groups, and Galois covers. The last two conjectures are still ...


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As far as I can see, your proof is entirely correct; however, it is not a proof of the full lonely runner conjecture, but rather a proof of a particular easy special case. In the original statement of the problems, the speeds of the runners are allowed to be arbitrary real numbers. It is a theorem that it is in fact enough to take the speeds of the ...



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