English

The largest prime factor of $X^3+2$

Number Theory 2014-12-03 v2

Abstract

Improving on a theorem of Heath-Brown, we show that if XX is sufficiently large then a positive proportion of the values {n3+2:n(X,2X]}\{n^3+2:n\in (X,2X]\} have a prime factor larger than X1+1052X^{1+10^{-52}}.

Keywords

Cite

@article{arxiv.1412.0024,
  title  = {The largest prime factor of $X^3+2$},
  author = {A. J. Irving},
  journal= {arXiv preprint arXiv:1412.0024},
  year   = {2014}
}

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15 pages