This article is from the Hofstadter and GEB FAQ, by TANAKA Tomoyuki tanaka@cs.indiana.edu with numerous contributions by others.
someone posted an outline of a solution to the problem of
expressing "b is a power of 10" (GEB, Page 215). that answer
used the Chinese Remainder Theorem. here's another approach:
http://einstein.et.tudelft.nl/~arlet/puzzles/sol.cgi/logic/hofstadter
http://www.cs.uu.nl/wais/html/na-faq/puzzles-archive-logic-part1.html
 
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