대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제45권1호
  • /
  • Pages.143-155
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  • 2008
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  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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ABOUT THE PERIOD OF BELL NUMBERS MODULO A PRIME

  • 발행 : 2008.02.29
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초록

Let p be a prime number. It is known that the order o(r) of a root r of the irreducible polynomial $x^p-x-l$ over $\mathbb{F}_p$ divides $g(p)=\frac{p^p-1}{p-1}$. Samuel Wagstaff recently conjectured that o(r) = g(p) for any prime p. The main object of the paper is to give some subsets S of {1,...,g(p)} that do not contain o(r).

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참고문헌

  1. N. Bourbaki, Elements de mathematique. Algebre. Chapitres 4 a 7, Lecture Notes in Mathematics, 864. Masson, Paris, 1981
  2. S. D. Cohen, Reducibility of sublinear polynomials over a finite field, Bull. Korean Math. Soc. 22 (1985), no. 1, 53-56
  3. R. Lidl and H. Niederreiter, Finite Fields, With a foreword by P. M. Cohn. Second edition. Encyclopedia of Mathematics and its Applications, 20. Cambridge University Press, Cambridge, 1997
  4. W. F. Lunnon, P. A. B. Pleasants, N. M. Stephens, Arithmetic properties of Bell numbers to a composite modulus. I, Acta Arith. 35 (1979), no. 1, 1-16 https://doi.org/10.4064/aa-35-1-1-16
  5. W. H. Mills, The degrees of the factors of certain polynomials over finite fields, Proc. Amer. Math. Soc. 25 (1970), 860-863
  6. S. Jr. Wagstaff, Aurifeuillian factorizations and the period of the Bell numbers modulo a prime, Math. Comp. 65 (1996), no. 213, 383-391 https://doi.org/10.1090/S0025-5718-96-00683-7

피인용 문헌

  1. Some primitive elements for the Artin–Schreier extensions of finite fields vol.210, pp.1, 2015, https://doi.org/10.1007/s10958-015-2548-5