A CLASS OF IRREDUCIBLE POLYNOMIALS ASSOCIATED WITH PRIME DIVISORS OF VALUES OF CYCLOTOMIC POLYNOMIALS. Issue 4 (2019) - Filaseta, Michael
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 $1\leqslant k\leqslant n$ is the reciprocal of the decimal number consisting of $k$ digits which are each $1$ . Similar results following from the same techniques are discussed.