For every n and odd prime p>n, the Wilson quotient modulo p^n is a finite sum of recursively defined integer polynomials evaluated at power sums of Fermat quotients.
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Wilson's theorem modulo higher prime powers I: Fermat and Wilson quotients
For every n and odd prime p>n, the Wilson quotient modulo p^n is a finite sum of recursively defined integer polynomials evaluated at power sums of Fermat quotients.