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Skolem-Mahler-Lech Theorem


If {a_0,a_1,...} is a recursive sequence, then the set of all k such that a_k=0 is the union of a finite (possibly empty) set and a finite number (possibly zero) of full arithmetical progressions, where a full arithmetic progression is a set of the form {r,r+d,r+2d,...} with r in [0,d).


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References

Lech, C. "A Note on Recurring Series." Ark. Mat. 2, 417-421, 1953.Myerson, G. and van der Poorten, A. J. "Some Problems Concerning Recurrence Sequences." Amer. Math. Monthly 102, 698-705, 1995.

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Skolem-Mahler-Lech Theorem

Cite this as:

Weisstein, Eric W. "Skolem-Mahler-Lech Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Skolem-Mahler-LechTheorem.html

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