http://www.google.com/search?hl=en&ie=ISO-8859-1&q=exp+pi+sqrt+integer
has some pages with explanations involving the Jacobi function J, elliptic
curves and other mathematical esoterica. Unfortunately it does not seem
likely that an explanation suitable for a college senior is available,
unless he is willing to educate himself for several months on higher
mathematics.
Hal Finney
> Exp(Pi*Sqrt(n)) Page
> This table lists values of Exp(Pi*Sqrt(n)), for some selected values of
> n up to 1000. Some of these values are very close to integers. A prize
> will be awarded to anyone who can either convincingly argue that this is
> coincidence, or who can explain why this is so in terms intelligible to
> an intelligent college senior. Something else that might help to lift
> the veil on this mystery would be a predictor: for a given value of n,
> is Exp(Pi*Sqrt(n)) close to an integer?
> ...
> 163 262537412640768743.9999999999992
> ...
Received on Fri Aug 09 2002 - 09:21:28 PDT