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A CLASS OF IRREDUCIBLE POLYNOMIALS ASSOCIATED WITH PRIME DIVISORS OF VALUES OF CYCLOTOMIC POLYNOMIALS

Part of: Polynomials and matrices Multiplicative number theory Algebraic number theory: global fields Sequences and sets General field theory

Published online by Cambridge University Press:  14 August 2019

Michael Filaseta
Michael Filaseta*
Affiliation:
Department of Mathematics, University of South Carolina, Columbia, SC 29208, U.S.A. email [email protected]
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Abstract

We prove that for every sufficiently large integer $n$, the polynomial $1+x+x^{2}/11+x^{3}/111+\cdots +x^{n}/111\ldots 1$ is irreducible over the rationals, where the coefficient of $x^{k}$ for $1\leqslant k\leqslant n$ is the reciprocal of the decimal number consisting of $k$ digits which are each $1$. Similar results following from the same techniques are discussed.

MSC classification

Primary: 11R09: Polynomials (irreducibility, etc.)
Secondary: 11C08: Polynomials 11B83: Special sequences and polynomials 11N05: Distribution of primes 12E05: Polynomials (irreducibility, etc.)
Type
Research Article
Information
Mathematika , Volume 65 , Issue 4 , 2019 , pp. 1033 - 1037
Copyright
Copyright © University College London 2019 

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References

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