On the p-divisibility of Fermat quotients

  title={On the p-divisibility of Fermat quotients},
  author={Reijo Ernvall and Tauno Mets{\"a}nkyl{\"a}},
  journal={Math. Comput.},
The authors carried out a numerical search for Fermat quotients Qa = (ap−1 − 1)/p vanishing mod p, for 1 ≤ a ≤ p − 1, up to p < 106. This article reports on the results and surveys the associated theoretical properties of Qa. The approach of fixing the prime p rather than the base a leads to some aspects of the theory apparently not published before. 

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