On the converse of Wolstenholme's Theorem

@article{McIntosh1995OnTC,
  title={On the converse of Wolstenholme's Theorem},
  author={Richard J. McIntosh},
  journal={Acta Arithmetica},
  year={1995},
  volume={71},
  pages={381-389}
}
The problem of distinguishing prime numbers from composite numbers (. . .) is known to be one of the most important and useful in arithmetic. (. . .) The dignity of the science itself seems to require that every possible means be explored for the solution of a problem so elegant and so celebrated. Wilson’s Theorem states that if p is prime then (p− 1)! ≡ −1 (mod p). It is easy to see that the converse of Wilson’s Theorem also holds. Thus Wilson’s Theorem can be used to identify the primes… Expand
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