ArticleOriginal scientific text

Title

On some arithmetical properties of middle binomial coefficients

Authors 1, 2

Affiliations

  1. Department of Mathematics and Computer Science, Ben-Gurion University, Beer-Sheva 84105, Israel
  2. Tracor Applied Sciences, Building 1-8, 6500 Tracor Lane, Austin, Texas 78725, U.S.A.

Bibliography

  1. [BG] D. Barbolosi et P. J. Grabner, Distribution des coefficients multinomiaux et q-binomiaux modulo p, Indag. Math. 7 (1996), 129-135.
  2. [E] P. Erdős, On some divisibility properties of {2nchsen}, Canad. Math. Bull. 7 (1964), 513-518.
  3. [EG] P. Erdős and R. L. Graham, Old and New Problems and Results in Combinatorial Number Theory, L'Enseignement Mathématique, Imprimerie Kundig, Geneva, 1980.
  4. P. Erdős, R. L. Graham, I. Z. Ruzsa and E. G. Straus, On the prime factors of {2nchsen}, Math. Comp. 29 (1975), 83-92.
  5. [EK] P. Erdős and G. Kolesnik, Prime power divisors of binomial coefficients, preprint.
  6. [Ga] A. Gardiner, Four problems on prime power divisibility, Amer. Math. Monthly 95 (1988), 926-931.
  7. [GW] R. Garfield and H. S. Wilf, The distribution of the binomial coefficients modulo p, J. Number Theory 41 (1992), 1-5.
  8. R. Graham, personal communication.
  9. A. Granville, Zaphod Beeblebrox's brain and the fifty-ninth row of Pascal's triangle, Amer. Math. Monthly 99 (1992), 318-331.
  10. [GR] A. Granville and O. Ramaré, Explicit bounds on exponential sums and the scarcity of squarefree binomial coefficients, Mathematika 43 (1996), 73-107.
  11. [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.
  12. [HS] E. Hexel and H. Sachs, Counting residues modulo a prime in Pascal's triangle, Indian J. Math. 20 (1978), 91-105.
  13. [Hey] H. Heyer, Probability Measures on Locally Compact Groups, Springer, Berlin, 1977.
  14. [KN] L. Kuipers and H. Niederreiter, Uniform Distribution of Sequences, Wiley, New York, 1974.
  15. [K] E. E. Kummer, Über die Ergänzungssätze zu den allgemeinen Reciprocitäts-gesetzen, J. Reine Angew. Math. 44 (1852), 93-146.
  16. [L] E. Lucas, Théorie des fonctions numériques simplement périodiques, Amer. J. Math. 1 (1878), 184-240, 289-321.
  17. [N] W. Narkiewicz, Uniform Distribution of Sequences of Integers in Residue Classes, Lecture Notes in Math. 1087, Springer, Berlin, 1984.
  18. [R] M. Rosenblatt, Markov Processes. Structure and Asymptotic Behavior, Springer, Berlin, 1971.
  19. [San] J. W. Sander, Prime power divisors of {2nchsen}, J. Number Theory 39 (1991), 65-74.
  20. [Sár] A. Sárközy, On divisors of binomial coefficients, I, J. Number Theory 20 (1985), 70-80.
  21. [V] G. Velammal, Is the binomial coefficient {2nchsen} squarefree?, Hardy-Ramanujan J. 18 (1995), 23-45.
Pages:
31-41
Main language of publication
English
Received
1997-01-29
Accepted
1997-08-18
Published
1998
Exact and natural sciences