A simple proof of the Skolem-Mahler-Lech theorem (Q1084125)
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scientific article; zbMATH DE number 3977080
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A simple proof of the Skolem-Mahler-Lech theorem |
scientific article; zbMATH DE number 3977080 |
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A simple proof of the Skolem-Mahler-Lech theorem (English)
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1986
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The author gives a simple proof of the following theorem, due to Skolem, Mahler, Lech: given a sequence \((a_n)\) which satisfies a linear recursion over a field of characteristic 0, the set \(\{n\in \mathbb{N}\mid a_n=0\}\) is ultimately periodic. The usual proofs use \(p\)-adic analysis. The proof of the author is elementary and self-contained.
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Skolem-Mahler-Lech theorem
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Skolem's p-adic method
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linear recursive sequence
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rational functions
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