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).