On the irreducibility of the non-cyclotomic part of most 0,1-polynomials with few terms

Abstract

We provide an alternative exposition of a result due to Schinzel. Fix an integer $k \ge 2$. For almost all choices of positive integers $n_{1} < \cdots < n_{k}$, we show that the polynomial $F(x) = 1 + x^{n_{1}} + \cdots + x^{n_{k}}$, removed of its cyclotomic factors, is irreducible.