The Sufficient Set of Congruences of Binomial Coefficients for Primality

Abstract

For any given integer $p$, we show that primality of $p$ is equivalent to $\lceil \frac{1}{2}{\log }_{2}p\rceil$ congruences of binomial coefficients modulo $p$. We also give extensions of this result to several other congruences that are similar in nature.

arXiv comment9 pages