Binomial coefficients coprime to 6
Pascal Jelinek
Abstract
It is a well known result by Singmaster that any integer d divides almost all binomial coefficients. The study of the structure and the size of the exceptional set has been of interest for many decades. In the case where d is a prime power, these sets are well understood and their size is known. However, if d has at least two distinct prime factors, no non-trivial bounds are known. In this paper, we will provide the first non trivial bound on the number of binomial coefficients coprime to 6.
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