Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Formulas for the number of binomial coefficients divisible by a fixed power of a prime


Author: F. T. Howard
Journal: Proc. Amer. Math. Soc. 37 (1973), 358-362
MSC: Primary 05A10; Secondary 10A99
MathSciNet review: 0309737
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Define $ {\theta _j}(n)$ as the number of binomial coefficients $ (\mathop s\limits^n )$ divisible by exactly $ {p^j}$. A formula for $ {\theta _2}(n)$ is found, for all n, and formulas for $ {\theta _j}(n)$ for $ n = a{p^k} + b{p^r}$ and $ n = {c_1}{p^{{k_1}}} + \cdots + {c_m}{p^{{k_m}}}({k_1} \geqq j,{k_{i + 1}} - {k_i} \geqq j\;{\text{for}}\;i = 1, \cdots ,m - 1)$ are derived.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 05A10, 10A99

Retrieve articles in all journals with MSC: 05A10, 10A99


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1973-0309737-X
PII: S 0002-9939(1973)0309737-X
Keywords: Binomial coefficient, prime number
Article copyright: © Copyright 1973 American Mathematical Society