[FOM] Joe Shipman's desired example

[Richard Pollack]

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

-- 
Ricky Pollack
Professor of Mathematics and Computer Science
Courant Institute of Mathematical Sciences/NYU
 Office: Room 716, Warren Weaver Hall (Courant
             Institute).
Phone: 212-998-3167
Fax: 212-995-4121
Mailing Address: 251 Mercer Street,
		            New York, NY 10012, U.S.A.
Email: pollack at cims,nyu.edu
homepage url:
    http://math.nyu.edu/faculty/pollack/index.html