Structured Solutions of Prime-Base Binomial Congruences

Gabriel Araújo Guedes, Ricardo Nunes Machado Junior

In this paper, we study the congruence $\left(\genfrac{}{}{0ex}{}{qn}{n}\right)\equiv q^n(\mathrm{mod}n)$ for a prime base $q$. Motivated by the OEIS sequence \seqnum{A080469} and the conjectural existence of inf…