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 as the number of binomial coefficients divisible by exactly . A formula for is found, for all *n*, and formulas for for and are derived.

**[1]**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**0249308****[2]**L. E. Dickson,*History of the theory of numbers*. Vol. 1, Publication no. 256, Carnegie Institution of Washington, Washington, D.C., 1919.**[3]**N. J. Fine,*Binomial coefficients modulo a prime*, Amer. Math. Monthly**54**(1947), 589–592. MR**0023257****[4]**F. T. Howard,*The number of binomial coefficients divisible by a fixed power of 2*, Proc. Amer. Math. Soc.**29**(1971), 236–242. MR**0302459**, 10.1090/S0002-9939-1971-0302459-9

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

Keywords:
Binomial coefficient,
prime number

Article copyright:
© Copyright 1973
American Mathematical Society