Let 
be a field of field
characteristic 0 (e.g., the rationals 
) and let 
be a sequence of elements
of 
which satisfies a difference equation of the form
 |
where the coefficients 
are fixed elements of 
. Then, for any 
, we have either 
for only finitely many values of 
, or 
for the values of 
in some arithmetic progression.
The proof involves embedding certain fields inside the p-adic numbers 
for some prime 
, and using properties of zeros of power
series over 
(Strassman's theorem).
