For P ∈ F2[z] with P (0) = 1 and deg(P ) ≥ 1, let A = A(P ) be the unique subset of N such that ∑ n≥0 p(A, n)zn ≡ P (z) (mod 2), where p(A, n) is the number of partitions of n with parts in A. Let p be an odd prime number, and let P be irreducible of order p ; i.e., p is the smallest positive integer such that P divides 1+ zp in F2[z]. N. Baccar proved that… (More)