The largest prime factor of $X^3+2$
Volume 171 / 2015
Acta Arithmetica 171 (2015), 67-80
MSC: 11N32, 11N36.
DOI: 10.4064/aa171-1-5
Abstract
Improving on a theorem of Heath-Brown, we show that if $X$ is sufficiently large then a positive proportion of the values $\{n^3+2:n\in (X,2X]\}$ have a prime factor larger than $X^{1+10^{-52}}$.
