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

Volume 171 / 2015

A. J. Irving Acta Arithmetica 171 (2015), 67-80 MSC: 11N32, 11N36. DOI: 10.4064/aa171-1-5


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 $X^{1+10^{-52}}$.


  • A. J. IrvingCentre de recherches math\'ematiques
    Universit\'ede Montr\'eal
    Pavillon Andr\'e-Aisenstadt
    2920 Chemin de la tour, room 5357
    Montr\'eal (Qu\'ebec) H3T 1J4, Canada

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