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A CLASS OF IRREDUCIBLE POLYNOMIALS ASSOCIATED WITH PRIME DIVISORS OF VALUES OF CYCLOTOMIC POLYNOMIALS
Published online by Cambridge University Press: 14 August 2019
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.
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- Copyright © University College London 2019