A CLASS OF IRREDUCIBLE POLYNOMIALS ASSOCIATED WITH PRIME DIVISORS OF VALUES OF CYCLOTOMIC POLYNOMIALS. Issue 4 (14th August 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: 2019-08-14
• 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 + ⋯ + x n / 111 … 1 is irreducible over the rationals, where the coefficient of x k for 1 ⩽ k ⩽ 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.