Gertsch quotient living in the “poor man’s adele ring” A: Kurepa-Bell-Wilson congruence

Abstract: This study examines Kurepa, Bell, and Wilson congruences for odd prime $p \geq 3$, focusing on the left factorial relation $K_p \equiv \mathbf{Bell}_{p-1} - 1 \pmod p$. We demonstrate that the Kurepa modulo $p$ naturally generates the Gertsch quotient $\mathbb{G}_p \coloneqq \frac{K_p - \mathbf{Bell}_{p-1} + 1}{p}$, which, for larger primes, resides in the poor man's adele ring $\mathcal{A}$.

number theory

Audience: researchers in the topic

Combinatorial and additive number theory seminar (CANT 2026)