Let λ denote Carmichael’s function, so λ(n) is the universal exponent for the multiplicative group modulo n. It is closely related to Euler’s φ-function, but we show here that the image of λ is much denser than the image of φ. In particular the number of λ-values to x exceeds for all large x, while for φ it is equal to , an old result of Erdős. We also improve on an earlier result of the first author and Friedlander giving an upper bound for the distribution of λ-values.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa162-3-6,
author = {Florian Luca and Carl Pomerance},
title = {On the range of Carmichael's universal-exponent function},
journal = {Acta Arithmetica},
volume = {166},
year = {2014},
pages = {289-308},
zbl = {1292.11109},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa162-3-6}
}
Florian Luca; Carl Pomerance. On the range of Carmichael's universal-exponent function. Acta Arithmetica, Tome 166 (2014) pp. 289-308. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa162-3-6/