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Tytuł artykułu

On some arithmetical properties of middle binomial coefficients

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EN
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Twórcy
  • Department of Mathematics and Computer Science, Ben-Gurion University, Beer-Sheva 84105, Israel
  • Tracor Applied Sciences, Building 1-8, 6500 Tracor Lane, Austin, Texas 78725, U.S.A.
Bibliografia
  • [BG] D. Barbolosi et P. J. Grabner, Distribution des coefficients multinomiaux et q-binomiaux modulo p, Indag. Math. 7 (1996), 129-135.
  • [E] P. Erdős, On some divisibility properties of ${2n \choose n}$, Canad. Math. Bull. 7 (1964), 513-518.
  • [EG] P. Erdős and R. L. Graham, Old and New Problems and Results in Combinatorial Number Theory, L'Enseignement Mathématique, Imprimerie Kundig, Geneva, 1980.
  • P. Erdős, R. L. Graham, I. Z. Ruzsa and E. G. Straus, On the prime factors of ${2n \choose n}$, Math. Comp. 29 (1975), 83-92.
  • [EK] P. Erdős and G. Kolesnik, Prime power divisors of binomial coefficients, preprint.
  • [Ga] A. Gardiner, Four problems on prime power divisibility, Amer. Math. Monthly 95 (1988), 926-931.
  • [GW] R. Garfield and H. S. Wilf, The distribution of the binomial coefficients modulo p, J. Number Theory 41 (1992), 1-5.
  • R. Graham, personal communication.
  • A. Granville, Zaphod Beeblebrox's brain and the fifty-ninth row of Pascal's triangle, Amer. Math. Monthly 99 (1992), 318-331.
  • [GR] A. Granville and O. Ramaré, Explicit bounds on exponential sums and the scarcity of squarefree binomial coefficients, Mathematika 43 (1996), 73-107.
  • [Hex] E. Hexel, Einige Bemerkungen zum Pascal'schen Dreieck modulo p, in Contributions to Graph Theory and its Applications (International Colloquium Oberhof, 1977), Technische Hochschule Ilmenau, Ilmenau, 1977, 121-128.
  • [HS] E. Hexel and H. Sachs, Counting residues modulo a prime in Pascal's triangle, Indian J. Math. 20 (1978), 91-105.
  • [Hey] H. Heyer, Probability Measures on Locally Compact Groups, Springer, Berlin, 1977.
  • [KN] L. Kuipers and H. Niederreiter, Uniform Distribution of Sequences, Wiley, New York, 1974.
  • [K] E. E. Kummer, Über die Ergänzungssätze zu den allgemeinen Reciprocitäts-gesetzen, J. Reine Angew. Math. 44 (1852), 93-146.
  • [L] E. Lucas, Théorie des fonctions numériques simplement périodiques, Amer. J. Math. 1 (1878), 184-240, 289-321.
  • [N] W. Narkiewicz, Uniform Distribution of Sequences of Integers in Residue Classes, Lecture Notes in Math. 1087, Springer, Berlin, 1984.
  • [R] M. Rosenblatt, Markov Processes. Structure and Asymptotic Behavior, Springer, Berlin, 1971.
  • [San] J. W. Sander, Prime power divisors of ${2n \choose n}$, J. Number Theory 39 (1991), 65-74.
  • [Sár] A. Sárközy, On divisors of binomial coefficients, I, J. Number Theory 20 (1985), 70-80.
  • [V] G. Velammal, Is the binomial coefficient ${2n \choose n}$ squarefree?, Hardy-Ramanujan J. 18 (1995), 23-45.
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Bibliografia
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