Abstract:

The Skolem-Mahler-Lech theorem states that if a sequences f(n) is given by a linear recurrence relation over a fields of characteristic 0, then the set of n such that f(n)=0 is the union of a finite set and a finite number of arithmetic progressions. In this talk, I will introduce some results on Skolem Problem (does the sequence has a zero?) and other two related problems for sequences given by linear recurrence relations.