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A CLASS OF IRREDUCIBLE POLYNOMIALS ASSOCIATED WITH PRIME DIVISORS OF VALUES OF CYCLOTOMIC POLYNOMIALS
Author(s) -
Filaseta Michael
Publication year - 2019
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579319000305
Subject(s) - mathematics , reciprocal , cyclotomic polynomial , prime (order theory) , integer (computer science) , class (philosophy) , decimal , polynomial , rational number , combinatorics , pure mathematics , arithmetic , mathematical analysis , philosophy , linguistics , artificial intelligence , computer science , programming language
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.