[FOM] Prime values of polynomials
joeshipman@aol.com
joeshipman at aol.com
Thu Feb 28 16:24:00 EST 2008
I have read that no integer-coefficient polynomials of degree >1 are
known to take infinitely many prime values; conjecturally, all the
irreducible ones do.
This is a nice example, but it's not so easy to tell whether a
polynomial is irreducible.
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? (Alternatively, I'll accept an example of a property which is
conjectured to hold for all members of a set X but is not known to hold
for any, where X is easier to recognize than "irreducible polynomials
of degree >1" even if X is not as easy to recognize as the integers
are).
-- JS
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