A binomial coefficient congruence modulo prime powers
type: Item
instance of: scholarly article
title: A binomial coefficient congruence modulo prime powers
zbMATH Open document ID: 0769.11008
published in: Journal of Number Theory
publication date: 1993-05-16T00:00:00Z
review text: The authors deduce from the main result of \textit{K. S. Davis} and \textit{W. A. Webb} [Eur. J. Comb. 11, 229-233 (1990; Zbl 0704.11002)], that if \(p\) is a prime \(>3\) and \(0\leq a\), \(b<p^ s\) then \[ {{np^{r+s}+a} \choose{kp^{r+s}+b}}\equiv {{np^{[r/3]}} \choose{kp^{[r/3]}}}{a \choose b}\pmod {p^{r+1}}. \]
reviewed by: Andrew Granville
Mathematics Subject Classification ID: 11B65
Mathematics Subject Classification ID: 11A07
Mathematics Subject Classification ID: 05A10
zbMATH DE Number: 166053
zbMATH Keywords: congruence modulo prime powers
zbMATH Keywords: binomial coefficients
zbMATH Keywords: Lucas' theorem
author: Kenneth S. Davis
author: William A. Webb
MaRDI profile type: Publication
full work available at URL: jnth.1993.1002
OpenAlex ID: W2052977281
DOI: 10.1006/JNTH.1993.1002
description: scientific article; zbMATH DE number 166053