Is the p-adic expansion of a rational number repating, and does every p-adic number with a repeating series correspond to a rational number?

Asked May 13 '23 at 18:13

Active May 13 '23 at 18:13

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Is the $p$-adic expansion of a rational number repeating after some point? Does every $p$-adic number with a series that is repeating after some point correspond to a rational number?

asked May 13 '23 at 18:13

schuelermine

Also e.g. https://math.stackexchange.com/q/4164508/96384. And look at Keith Conrad's comprehensive blurb https://kconrad.math.uconn.edu/blurbs/gradnumthy/rationalsinQp.pdf – Torsten Schoeneberg May 13 '23 at 22:07

Is the p-adic expansion of a rational number repating, and does every p-adic number with a repeating series correspond to a rational number?

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