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