We improve known bounds for the maximum number of pairwise disjoint arithmetic progressions using distinct moduli less than x. We close the gap between upper and lower bounds even further under the assumption of a conjecture from combinatorics about Δ-systems (also known as sunflowers).
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa157-4-5,
author = {R\'egis de la Bret\`eche and Kevin Ford and Joseph Vandehey},
title = {On non-intersecting arithmetic progressions},
journal = {Acta Arithmetica},
volume = {161},
year = {2013},
pages = {381-392},
zbl = {06136635},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa157-4-5}
}
Régis de la Bretèche; Kevin Ford; Joseph Vandehey. On non-intersecting arithmetic progressions. Acta Arithmetica, Tome 161 (2013) pp. 381-392. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa157-4-5/