Bernd C. Kellner

collaborators

3 papers

math.NT2025

Wilson's theorem modulo higher prime powers III: The cases modulo $p^{6}$ and $p^{7}$

Bernd C. Kellner

Extending previous work of the author, we compute the Wilson quotient modulo $p^{5}$ and $p^{6}$ , and equivalently $(p - 1)!$ modulo $p^{6}$ and $p^{7}$ , respectively. Further, we determine…

math.NT2025

Wilson's theorem modulo higher prime powers II: Bernoulli numbers and polynomials

Bernd C. Kellner

By recent work of the author, Wilson's theorem as well as the Wilson quotient can be described by supercongruences of power sums of Fermat quotients modulo every higher prime power…

math.NT2025

Wilson's theorem modulo higher prime powers I: Fermat and Wilson quotients

Bernd C. Kellner

We show that Wilson's theorem as well as the Wilson quotient can be described by supercongruences modulo any higher prime power involving terms of power sums of Fermat quotients. T…

Wilson's theorem modulo higher prime powers III: The cases modulo p6 and p7

Wilson's theorem modulo higher prime powers II: Bernoulli numbers and polynomials

Wilson's theorem modulo higher prime powers I: Fermat and Wilson quotients

Wilson's theorem modulo higher prime powers III: The cases modulo $p^{6}$ and $p^{7}$