# p-Adic Continued Fractions

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.

p

[,,…]

a

1

a

2

p

||≤p/2

a

i

p

p

p

a/b

p

a

b