Bakir FARHI : Professeur à l'ENSM (Alger)
  1. B. Farhi, Expansion of a bivariate symmetric mean in the neighborhood of the first bisector, arXiv:2506.07601v1 [math.NT] 9 Jun 2025.
  2. B. Farhi, Formulas involving Bernoulli and Stirling numbers of both kinds, J. Integer Sequences, 28 2025, Article 25.2.6.
  3. B. Farhi, q-analogues of sums of consecutive powers of natural numbers and extended Carlitz q-Bernoulli numbers and polynomials, arXiv:2501.02499v1 [math.NT] 5 Jan 2025.
  4. B. Farhi, Some applications of the Lagrange inversion formula for the k-Fibonacci numbers, J. Integer Sequences, 27 2024, Article 24.1.1.
  5. B. Farhi, Characterization of the Bernoulli polynomials via the Raabe functional equation, Aequationes Math., 98 (3) 2024, p. 787-801.
  6. B. Farhi, Nontrivial lower bounds for the p-adic valuations of some type of rational numbers and an application for establishing the integrality of some rational sequences, Notes Number Theory Discrete Math., vol. 29, n°4 2023, p. 820-826.
  7. B. Farhi, Nontrivial Lower Bounds for the p-adic Valuation of Certain Rational Numbers, J. Integer Sequences, 26 2023, Article 23.6.1.
  8. B. Farhi, On the sum of the values of a polynomial at natural numbers which form a decreasing arithmetic progression, Indian J. Pure Appl. Math., 54 2023, p. 15-27. (En hommage à Ibn al-Banna al-Marrakushi à l'occasion du 7ème centenaire de sa mort).
  9. B. Farhi, Results and conjectures related to a conjecture of Erdős concerning primitive sequences, Asian-Eur. J. Math., Vol. 16, No. 02, 2350018 2023.
  10. A. Bedhouche & B. Farhi, On some products taken over the prime numbers, J. Integer Sequences, 26 2023, Article 23.1.5.
  11. B. Farhi, The integrality of the Genocchi numbers obtained through a new identity and other results, Notes Number Theory Discrete Math., vol. 28, n°4 2022, p. 749-757.
  12. B. Farhi, A new generalization of the Genocchi numbers and its consequence on the Bernoulli polynomials, Adv. Pure Appl. Math., vol. 13, n°4 2022, p. 18-28.
  13. B. Farhi, Arithmetic properties of the Genocchi numbers and their generalization, arXiv: 2103.07890v1 [math.NT] 14 Mar 2021.
  14. B. Farhi, Nontrivial effective lower bounds for the least common multiple of a q-arithmetic progression, J. Integer Sequences, 24 2021, Article 21.3.7.
  15. S.A. Bousla & B. Farhi, Identités et estimations concernant le plus petit commun multiple de suites à forte divisibilité, C. R. Math, 358, n°4, 2020, p. 481-487.
    Détaillé dans arXiv: 1907.06700v1 [math.NT] (15 Jul 2019).
  16. S.A. Bousla & B. Farhi, Nontrivial effective lower bounds for the least common multiple of some quadratic sequences, J. Integer Sequences, 23 2020, Article 20.6.6.
  17. B. Farhi, On the derivatives of the integer-valued polynomials, Funct. Approx. Comment. Math, 61, Number 2 2019, p. 227-241.
  18. B. Farhi, Summation of certain infinite Lucas-related series, J. Integer Sequences, 22 2019, Article 19.1.6.
  19. B. Farhi, On the possible quantities of Fibonacci numbers that occur in some types of intervals, Acta Math. Univ. Comenianae, 87 (2) 2018, p. 291-299.
  20. B. Farhi, On the representation of an even perfect number as the sum of five cubes, Funct. Approx. Comment. Math, 57, Number 2 2017, p. 277-278. Détaillé dans arXiv: 1504.07322v1 (27 Apr 2015).
  21. B. Farhi, A measure of intelligence of an approximation of a real number in a given model, arXiv: 1703.01345v1 [math.GM] 1 Mar 2017.
  22. B. Farhi, Summation of certain infinite Fibonacci related series, arXiv: 1512.09033v1 30 Dec 2015.
  23. B. Farhi, An elementary proof that any natural number can be written as the sum of three terms of the sequence [n2/3], J. Integer Sequences, 17 2014, Article 14.7.6.
  24. B. Farhi, Algebraic and topological structures on the set of mean functions and generalization of the AGM mean, Colloq. Math, 132 2013, p. 139-149.
    Détaillé dans arXiv: 1002.4757v1 (25 Feb 2010).
  25. B. Farhi, On the representation of the natural numbers as the sum of three terms of the sequence [n2/a], J. Integer Sequences, 16 2013, Article 13.6.4.
  26. B. Farhi, A study of a curious arithmetic function, J. Integer Sequences, 15 2012, Article 12.3.1.
  27. B. Farhi, An explicit formula generating the non-Fibonacci numbers, arXiv: 1105.1127v2 10 May 2011.
  28. B. Farhi, How to obtain the continued fraction convergents of the number e by neglecting integrals, arXiv: 1005.2951v2 19 May 2010.
  29. B. Farhi, An analog of the arithmetic triangle obtained by replacing the products by the least common multiples, arXiv: 1002.1383v2 9 Feb 2010.
  30. B. Farhi, On the average asymptotic behavior of a certain type of sequences of integers, Integers : Electronic Journal of Combinatorial Number Theory, 9 2009, p. 555-567 (#A42).
  31. B. Farhi, An identity involving the least common multiple of binomial coefficients and its application, Amer. Math. Monthly, 116 2009, p. 836-839.
  32. B. Farhi, Formulas generating prime numbers under Cramér's conjecture, Elem. der Math, 64 2009, p. 45-52.
  33. B. Farhi & Daniel Kane, New results on the least common multiple of consecutive integers, Proc. Am. Math. Soc, 137 2009, p. 1933-1939.
  34. B. Farhi, A curious result related to Kempner's series, Amer. Math. Monthly, 115 2008, p. 933-938.
  35. B. Farhi, Upper bounds for the order of an additive basis obtained by removing a finite subset of a given basis, J. Number Theory, 128 2008, p. 2214-2230.
  36. B. Farhi, Nontrivial lower bounds for the least common multiple of some finite sequences of integers, J. Number Theory, 125 2007, p. 393-411.
  37. B. Deschamps & B. Farhi, Essentialités dans les bases additives, J. Number Theory, 123 2007, p. 170-192.
  38. B. Farhi, Sur l'ensemble exceptionnel de Weyl, C. R. Acad. Sci. Paris, Sér. I 343 2006, p. 441-445.
  39. B. Farhi, Minorations non triviales du plus petit commun multiple de certaines suites finies d'entiers, C. R. Acad. Sci. Paris, Sér. I 341 2005, p. 469-474.
  40. B. Farhi, Un analogue elliptique du théorème de Roth, C. R. Acad. Sci. Paris, Sér. I 341 2005, p. 275-278.
  41. B. Farhi, Une approche polynomiale du théorème de Faltings, C. R. Acad. Sci. Paris, Sér. I 340 2005, p. 103-106.





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