Author: N. Baccar 1
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  • 1 Université de Monastir I. P. E. I. M., Dép. de Math. Avenue de l’environnement 5000 Monastir, Tunisie France
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Abstract  

For P

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[z] with P(0) = 1 and deg(P) ≥ 1, let
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=
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(P) (cf. [4], [5], [13]) be the unique subset of ℕ such that Σn≥0p(
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, n)znP(z) (mod 2), where p(
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, n) is the number of partitions of n with parts in
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. Let p be an odd prime and P
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[z] be some irreducible polynomial of order p, i.e., p is the smallest positive integer such that P(z) divides 1 + zp in
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[z]. In this paper, we prove that if m is an odd positive integer, the elements of
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=
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(P) of the form 2km 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.

  • Impact Factor (2019): 0.693
  • Scimago Journal Rank (2019): 0.412
  • SJR Hirsch-Index (2019): 20
  • SJR Quartile Score (2019): Q3 Mathematics (miscellaneous)
  • Impact Factor (2018): 0.664
  • Scimago Journal Rank (2018): 0.412
  • SJR Hirsch-Index (2018): 19
  • SJR Quartile Score (2018): Q2 Mathematics (miscellaneous)

Manuscript Submission: HERE