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arXiv · 2608.27493

The Sufficient Set of Congruences of Binomial Coefficients for Primality

Zubeyir Cinkir
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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.

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Zubeyir Cinkir. 2026-08-26. The Sufficient Set of Congruences of Binomial Coefficients for Primality. https://arxiv.org/abs/2608.27493

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