Derivatives and irreducible polynomials (Q1871654)
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scientific article; zbMATH DE number 1903688
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Derivatives and irreducible polynomials |
scientific article; zbMATH DE number 1903688 |
Statements
Derivatives and irreducible polynomials (English)
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4 May 2003
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A simple proof, using derivatives, is presented of the following assertion: if a polynomial \(f\in \mathbb Z[X]\) has \(n\) distinct roots, each of order \(\geq2\), then \(f+1\) and \(f-1\) have irreducible factors of degree \(\geq n\). If, moreover, \(\deg f\leq 3n-1\), and \(f+1\) has no real roots, then it is irreducible.
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polynomials
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irreducibility criteria
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