On Lerch's formula for the Fermat quotient
Number Theory
2017-04-04 v6
Abstract
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.
Cite
@article{arxiv.1103.3907,
title = {On Lerch's formula for the Fermat quotient},
author = {John Blythe Dobson},
journal= {arXiv preprint arXiv:1103.3907},
year = {2017}
}
Comments
10 tables (at end)