The number of binomial coefficients divisible by a fixed power of $2$
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- by F. T. Howard
- Proc. Amer. Math. Soc. 29 (1971), 236-242
- DOI: https://doi.org/10.1090/S0002-9939-1971-0302459-9
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Abstract:
Define $f(n,j)$ as the number of binomial coefficients $\left ( {\begin {array}{*{20}{c}} n \\ r \\ \end {array} } \right )$ divisible by exactly ${2^j}$. We find formulas for $f(n,j)$ for $0 \leqq j \leqq 4$ and evaluate $f(n,j)$ for special values of n.References
- L. Carlitz, The number of binomial coefficients divisible by a fixed power of a prime, Rend. Circ. Mat. Palermo (2) 16 (1967), 299–320. MR 249308, DOI 10.1007/BF02843799 L. E. Dickson, History of the theory of numbers. Vol. 1, reprint, Chelsea, New York, 1952.
- F. T. Howard, A combinatorial problem and congruences for the Rayleigh function, Proc. Amer. Math. Soc. 26 (1970), 574–578. MR 266853, DOI 10.1090/S0002-9939-1970-0266853-6
- John Riordan, An introduction to combinatorial analysis, Wiley Publications in Mathematical Statistics, John Wiley & Sons, Inc., New York; Chapman & Hall, Ltd., London, 1958. MR 0096594
Bibliographic Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 29 (1971), 236-242
- MSC: Primary 05A10
- DOI: https://doi.org/10.1090/S0002-9939-1971-0302459-9
- MathSciNet review: 0302459