[FOM] Joe Shipman's desired example

Richard Pollack pollack at cims.nyu.edu
Thu Mar 6 10:08:45 EST 2008

Joe Shipman asked "Can anyone provide a comparably simple example of a
property which is believed to hold for all integers, but which is not
known to hold for any?"

I know of no such example but believe that there is none as the first
(and perhaps most important) step in discovering and possibly proving
a theorem in elementary arithmetic is to notice a property which holds
for some small integers and then after some thought might become a
conjecture (think of the oldest (biblical?) unresolved conjecture
about the evenness of all perfect numbers).


Ricky Pollack
Professor of Mathematics and Computer Science
Courant Institute of Mathematical Sciences/NYU
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Email: pollack at cims,nyu.edu
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