Perfect numbers, Wieferich primes and the solutions of $\left(\genfrac{}{}{0ex}{}{2n}{n}\right)\equiv 2^n\mathrm{mod}n$

Gabriel Guedes, Ricardo Machado

In this article we focus on the solutions of a congruence equation: $\left(\genfrac{}{}{0ex}{}{2n}{n}\right)\equiv 2^n\mathrm{mod}n$. Using the main result of this article and the SageMath software, we improve l…