Corpus ID: 119607968

On Lerch's formula for the Fermat quotient

@article{Dobson2011OnLF,
  title={On Lerch's formula for the Fermat quotient},
  author={J. Dobson},
  journal={arXiv: Number Theory},
  year={2011}
}
  • J. Dobson
  • Published 2011
  • Mathematics
  • arXiv: Number Theory
This paper explores some previously-unrecognized consequences of Lerch's 1905 formula for the Fermat quotient, with special attention to the sums which he introduced in this context. A generalization of his result is proved, and a new proof given of a sharpened result by Skula (2008). We also sharpen the criteria given by Emma Lehmer in 1938 for a Wieferich prime to be simultaneously a Mirimanoff prime. 

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