Sequences of {0,1}-polynomials with exponents in arithmetic progression - Finch, Carrie E. (MATHEMATICA SCANDINAVICA, 2012)
This paper finds the first irreducible polynomial in the sequence f_1(x), f_2(x), …, where f_k(x) = 1 + _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.