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