On Lerch's formula for the Fermat quotient

Details On Lerch's formula for the Fermat quotient On Lerch's formula for the Fermat quotient

2011-03-21

arxiv.org/abs/1103.3907v2

Mathematics

Number Theory

20 pages, 1 table (at end)

Scientific paper

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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