A CLASS OF IRREDUCIBLE POLYNOMIALS ASSOCIATED WITH PRIME DIVISORS OF VALUES OF CYCLOTOMIC POLYNOMIALS. Issue 4 (2019)

• Record Type: Journal Article
• Authors: Filaseta, Michael
• Is Part Of: Mathematika. Volume 65:Issue 4(2019)
• Page Start: 1033
• Page End: 1037
• Publication Date: 2019
• Subjects: 11R09 (primary), -- 11C08, -- 11B83, -- 11N05, -- 12E05 (secondary); Mathematics -- Periodicals; 510.5
• DOI: 10.1112/S0025579319000305
• Languages: English
• ISSNs: 0025-5793

Abstract

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.