Off the top of my head The last n digits of a^k (base b), left-zero-padded to n digits, are periodic in k if gcd(a, b) = 1, and ultimately periodic otherwise. The first n digits of a^k (base b), right-zero-padded to n digits, are periodic in k if a and b have a common integer power, and nonperiodic otherwise. ----- Original Message ----- From: "David Gale" <gale@math.berkeley.edu> To: "math-fun" <math-fun@mailman.xmission.com> Sent: Thursday, February 24, 2005 2:52 AM Subject: Re: [math-fun] not proven: 2^86
By the way, the first n digits are in fact not just eventually periodic, they're periodic, period. N'est-ce pas?
-- No virus found in this outgoing message. Checked by AVG Anti-Virus. Version: 7.0.300 / Virus Database: 266.4.0 - Release Date: 2/22/2005