TY - JOUR AU - Finch, Carrie E. PY - 2012/03/01 Y2 - 2024/03/28 TI - Sequences of $\{0,1\}$-polynomials with exponents in arithmetic progression JF - MATHEMATICA SCANDINAVICA JA - Math. Scand. VL - 110 IS - 1 SE - Articles DO - 10.7146/math.scand.a-15197 UR - https://www.mscand.dk/article/view/15197 SP - 75-81 AB - This paper finds the first irreducible polynomial in the sequence $f_1(x)$, $f_2(x), \ldots$, where $f_k(x) = 1 + \sum_{i=0}^k x^{n+id}$, based on the values of $n$ and $d$. In particular, when $d$ and $n$ are distinct, the author proves that if $p$ is the smallest odd prime not dividing $d-n$, then $f_{p-2}(x)$ is irreducible, except in a few special cases. The author also completely characterizes the appearance of the first irreducible polynomial, if any, when $d=n$. ER -