Hi Saibal,
Very interesting! I didn't know that one.
The chances that this is just a coincidence seems very low,
but
1) it should be verified whether this property holds to
much larger numbers,
which should be no problem with nowadays
computers,
2) Whether it holds to other bases, e.g
Hal Finney wrote: ``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.´´
I suspect that Roy Williams Clickery included this condition so that he
always has an e
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 h
Exp(Pi*Sqrt(n)) PageThis 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
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