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