View More View Less
  • 1 Preparatory Institut of Engineering Studies of Tunis, Montfleury, Tunisia
  • 2 University College of Jammum, Department of Mathematics, Saudi Arabia
Restricted access

Purchase article

USD  $25.00

1 year subscription (Individual Only)

USD  $800.00


Let N be a positive integer, A be a subset of ℚ and α=α1α2A\{0,N}. N is called an α-Korselt number (equivalently α is said an N-Korselt base) if α2pα1 divides α2Nα1 for every prime divisor p of N. By the Korselt set of N over A, we mean the set AKS(N) of all αA\{0,N} such that N is an α-Korselt number.

In this paper we determine explicitly for a given prime number q and an integer l ∈ ℕ \{0, 1}, the set A-KS(ql) and we establish some connections between the ql -Korselt bases in ℚ and others in ℤ. The case of A=[1,1[ is studied where we prove that ([1,1[)-KS(ql) is empty if and only if l = 2.

Moreover, we show that each nonzero rational α is an N-Korselt base for infinitely many numbers N = ql where q is a prime number and l ∈ ℕ.

  • [1]

    Beeger, N. G. W. H., On composite numbers n for which an −1 ≡ 1 (mod n) for every a prime to n, Scripta Math., 16 (1950), 133135.

    • Search Google Scholar
    • Export Citation
  • [2]

    Bouallegue, K., Echi, O. and Pinch, R., Korselt Numbers and Sets, Int. J. Number Theory, 6 (2010), 257269.

  • [3]

    Carmichael, R. D., Note on a new number theory function, Bull. Amer. Math. Soc., 16 (1910), 232238.

  • [4]

    Carmichael, R. D., On composite numbers P which satisfy the Fermat congruence aP −1 ≡ 1 (mod P), Amer. Math. Monthly, 19 (1912), 2227.

    • Search Google Scholar
    • Export Citation
  • [5]

    Echi, O., Williams Numbers, Mathematical Reports of the Academy of Sciences of the Royal Society of Canada, 29 (2) (2007), 4147.

  • [6]

    Echi, O. and Ghanmi, N., The Korselt Set of pq, Int. J. Number Theory., 8 (2) (2012), 299309.

  • [7]

    El-Rassasi, I., The Korselt set of the square of a prime, Int. J. Number Theory, 10 (4) (2014), 875884.

  • [8]

    Ghanmi, N., ℚ-Korselt Numbers, Turk. J. Math, 42 (2018), 27522762.

  • [9]

    Korselt, A., Problème chinois, L'intermediaire des Mathématiciens, 6 (1899), 142143.

The author instruction is available in PDF.

Please, download the file from HERE

Manuscript submission: HERE


  • Impact Factor (2019): 0.486
  • Scimago Journal Rank (2019): 0.234
  • SJR Hirsch-Index (2019): 23
  • SJR Quartile Score (2019): Q3 Mathematics (miscellaneous)
  • Impact Factor (2018): 0.309
  • Scimago Journal Rank (2018): 0.253
  • SJR Hirsch-Index (2018): 21
  • SJR Quartile Score (2018): Q3 Mathematics (miscellaneous)

Language: English, French, German

Founded in 1966
Publication: One volume of four issues annually
Publication Programme: 2020. Vol. 57.
Indexing and Abstracting Services:

  • CompuMath Citation Index
  • Mathematical Reviews
  • Referativnyi Zhurnal/li>
  • Research Alert
  • Science Citation Index Expanded (SciSearch)/li>
  • The ISI Alerting Services


Subscribers can access the electronic version of every printed article.

Senior editors

Editor(s)-in-Chief: Pálfy Péter Pál

Managing Editor(s): Sági, Gábor

Editorial Board

  • Biró, András (Number theory)
  • Csáki, Endre (Probability theory and stochastic processes, Statistics)
  • Domokos, Mátyás (Algebra (Ring theory, Invariant theory))
  • Győri, Ervin (Graph and hypergraph theory, Extremal combinatorics, Designs and configurations)
  • O. H. Katona, Gyula (Combinatorics)
  • Márki, László (Algebra (Semigroup theory, Category theory, Ring theory))
  • Némethi, András (Algebraic geometry, Analytic spaces, Analysis on manifolds)
  • Pach, János (Combinatorics, Discrete and computational geometry)
  • Rásonyi, Miklós (Probability theory and stochastic processes, Financial mathematics)
  • Révész, Szilárd Gy. (Analysis (Approximation theory, Potential theory, Harmonic analysis, Functional analysis))
  • Ruzsa, Imre Z. (Number theory)
  • Soukup, Lajos (General topology, Set theory, Model theory, Algebraic logic, Measure and integration)
  • Stipsicz, András (Low dimensional topology and knot theory, Manifolds and cell complexes, Differential topology)
  • Szász, Domokos (Dynamical systems and ergodic theory, Mechanics of particles and systems)
  • Tóth, Géza (Combinatorial geometry)

Gábor Sági
Address: P.O. Box 127, H–1364 Budapest, Hungary
Phone: (36 1) 483 8344 ---- Fax: (36 1) 483 8333