@article{Finch_2012, title={Sequences of $\{0,1\}$-polynomials with exponents in arithmetic progression}, volume={110}, url={https://www.mscand.dk/article/view/15197}, DOI={10.7146/math.scand.a-15197}, abstractNote={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 $d=n$.}, number={1}, journal={MATHEMATICA SCANDINAVICA}, author={Finch, Carrie E.}, year={2012}, month={Mar.}, pages={75–81} }