Improving on a theorem of Heath-Brown, we show that if X is sufficiently large then a positive proportion of the values n³ + 2: n ∈ (X,2X] have a prime factor larger than .
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa171-1-5,
author = {A. J. Irving},
title = {The largest prime factor of X$^3$ + 2},
journal = {Acta Arithmetica},
volume = {168},
year = {2015},
pages = {67-80},
zbl = {06487226},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa171-1-5}
}
A. J. Irving. The largest prime factor of X³ + 2. Acta Arithmetica, Tome 168 (2015) pp. 67-80. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa171-1-5/