# p-Adic Continued Fractions

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The -adic continued fraction of a -adic number is similar to the usual (simple) continued fraction in the reals with the requirement that . Since the rational numbers are a subset of the -adics, every rational number has a unique -adic continued fraction (which can be shown to be finite). This Demonstration computes the -adic continued fractions for all rational numbers of the form where is less than 1000 and and are positive integers less than or equal to 100.

Contributed by: Eric Errthum (March 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

J. Browkin, "Continued Fractions in Local Fields I," *Demonstratio Mathematica*, 11(1), 1978 pp. 67–82.

## Permanent Citation

"p-Adic Continued Fractions"

http://demonstrations.wolfram.com/PAdicContinuedFractions/

Wolfram Demonstrations Project

Published: March 7 2011