caa a22 4500 463171586 CHVBK 20180406164814.0 cr unu---uuuuu 170326e20071101xx s 000 0 eng 10.1007/s10998-007-4197-0 doi (NATIONALLICENCE)springer-10.1007/s10998-007-4197-0 Baccar N. I. P. E. I. M., Dép. de Math. Avenue de l'environnement, Université de Monastir, 5000, Monastir, Tunisie, France aut Sets with even partition functions and 2-adic integers [Elektronische Daten] [N. Baccar] For P ∊ $$ \mathbb{F}_2 $$ [z] with P(0) = 1 and deg(P) ≥ 1, let $$ \mathcal{A} $$ = $$ \mathcal{A} $$ (P) (cf. [4], [5], [13]) be the unique subset of ℕ such that Σ n≥0 p( $$ \mathcal{A} $$ , n)z n ≡ P(z) (mod 2), where p( $$ \mathcal{A} $$ , n) is the number of partitions of n with parts in $$ \mathcal{A} $$ . Let p be an odd prime and P ∊ $$ \mathbb{F}_2 $$ [z] be some irreducible polynomial of order p, i.e., p is the smallest positive integer such that P(z) divides 1 + z p in $$ \mathbb{F}_2 $$ [z]. In this paper, we prove that if m is an odd positive integer, the elements of $$ \mathcal{A} $$ = $$ \mathcal{A} $$ (P) of the form 2 k m are determined by the 2-adic expansion of some root of a polynomial with integer coefficients. This extends a result of F. Ben Saïd and J.-L. Nicolas [6] to all primes p. Springer Science+Business Media B.V., 2007 partitions nationallicence periodic sequences nationallicence order of a polynomial nationallicence cyclotomic polynomials nationallicence resultant nationallicence 2-adic integers nationallicence the Graeffe transformation nationallicence Periodica Mathematica Hungarica Springer Netherlands 55/2(2007-11-01), 197-213 0031-5303 55:2<197 2007 55 10998 https://doi.org/10.1007/s10998-007-4197-0 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10998-007-4197-0 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Baccar N. I. P. E. I. M., Dép. de Math. Avenue de l'environnement, Université de Monastir, 5000, Monastir, Tunisie, France aut NATIONALLICENCE 773 0- Periodica Mathematica Hungarica Springer Netherlands 55/2(2007-11-01), 197-213 0031-5303 55:2<197 2007 55 10998 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer