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There are interesting open problems concerning the polynomials in S. Using the main result in [1] (with base 2) or using the well-known explicit formula for the number of irreducible polynomials of degree ≤ n modulo 2, one can easily show that there are at least on the order of 2/n irreducible polynomials in Sn. Odlyzko (private communication) has asked whether almost all polynomials in S are irreducible. In other words, does

Squarefree values of polynomials all of whose coefficients are 0 and 1