A primality criterion based on a Lucas' congruence

Romeo Mestrovic

Let $p$ be a prime. In 1878 É. Lucas proved that the congruence $$\left(\genfrac{}{}{0ex}{}{p-1}{k}\right)\equiv (-1{)}^k(\mathrm{mod}p)$$ holds for any nonnegative integer $k\in \{0,1,\dots ,p-1\}$. The converse st…