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


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



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