The $p$ -adic Duffin--Schaeffer conjecture

preprint2022arXivOpen access

We prove Haynes' version of the Duffin--Schaeffer conjecture for the $p$ -adic numbers. In addition, we prove several results about an associated related but false conjecture, related to $p$ -adic approximation in the spirit of Jarník and Lutz.

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The $p$ -adic Duffin--Schaeffer conjecture

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The ppp-adic Duffin--Schaeffer conjecture

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The $p$ -adic Duffin--Schaeffer conjecture