On the number of roots of an integral polynomial modulo \(q\) (Q1273184)
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scientific article; zbMATH DE number 1229651
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the number of roots of an integral polynomial modulo \(q\) |
scientific article; zbMATH DE number 1229651 |
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On the number of roots of an integral polynomial modulo \(q\) (English)
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23 June 1999
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The authors prove that the set of congruence classes modulo a power of a prime number which are roots of an integral polynomial with degree \(d\) is a collection of at most \(d\) arithmetical progressions. This result implies an upper bound on the number of these roots lying in a given small interval; such bounds are useful to study the number of points close to a smooth algebraic curve. The methods of proofs are combinatorial and make no use of Hensel's Lemma.
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roots of polynomials
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congruences
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arithmetical progressions
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