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

2025/10/30 by Kellner, Bernd C.
#11B65 #11B68 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2510.26743

Abstract

Extending previous work of the author, we compute the Wilson quotient modulo p5 and p6, and equivalently (p-1)! modulo p6 and p7, respectively. Further, we determine some power sums of the Fermat quotients up to modulo p6. Subsequently, we discuss some patterns that occur in the p-adic coefficients of the Wilson quotient as well as of (p-1)!, whereby the original congruence (p-1)! ≡ -1 \pmodp fits perfectly into the theory.

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