Skolem-Mahler-Lerch Theorem
If 
is a Recurrence Sequence, then the set of all 
such that 
is the union of a finite(possibly Empty) set and a finite number (possibly zero) of full arithmetical progressions, where a fullarithmetic progression is a set of the form 
with 
References
Myerson, G. and van der Poorten, A. J. ``Some Problems Concerning Recurrence Sequences.'' Amer. Math. Monthly 102, 698-705, 1995.
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