On prime values of cyclotomic polynomials (Q2905851)
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scientific article; zbMATH DE number 6073177
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On prime values of cyclotomic polynomials |
scientific article; zbMATH DE number 6073177 |
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28 August 2012
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cyclotomic polynomial
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primes
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irreducibility
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math.NT
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On prime values of cyclotomic polynomials (English)
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Let \(\Phi_n(X)\) denoted the \(n\)th cyclotomic polynomial. The author shows, using only elementary arguments, that \(\Phi_k(X^n)\) is irreducible over the rationals iff \(\prod_{p|n}p\) divides \(k\), where \(p\) ranges over the prime divisors of \(n\). The author starts his discussion from scratch using many examples, making the paper accessible even to second year university students.
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