January 24, 2001 Eric Rasmusen notes, erasmuse@indiana.edu Http://Php.Indiana.edu/~erasmuse 44. Philip Davis, Reuben Hersh & Elena Marchisotto,"The Creation of New Mathematics: An Application of the Lakatos Heuristic," pp. 291-298 of The Mathematical Experience, Boston: Houghton-Mifflin (1981). p. 224. In the proof of the theorem at the top of the page, remember that Q=0 is allowed. The conjecture that p=q is the condition for magic numbers is indeed a sufficient condition. It is not both necessary *and* sufficient, though, which is what we're looking for here. p. 225. 1,2,5,25 and 125 are 1, 2^1, 5^1, 5^2, and 5^3, using the h- values just found to be valid.