Generalizations of a theorem about the binomial coefficient

Abstract

The object of this paper is to generalize a theorem on the binomial coefficient [4] to the case in an arithmetic progression. We will also give a slightly stronger result than Langevin's [2].

The title is changed. The paper has been improved and shortened. JP Journal of Algebra and Number Theory 14(2) (2009), 177-184, to appear. The paper "Generalizations of Several Theorems about the Binomial Coefficient and Grimm Conjecture" is available at arXiv:0901.3691v1