On the largest prime factor of n!+2 n -1
Journal de Théorie des Nombres de Bordeaux, Tome 17 (2005) no. 3, pp. 859-870.

Pour un entier n2, notons P(n) le plus grand facteur premier de n. Nous obtenons des majorations sur le nombre de solutions de congruences de la forme n!+2 n -10(modq) et nous utilisons ces bornes pour montrer que

lim supnP(n!+2n-1)/n(2π2+3)/18.

For an integer n2 we denote by P(n) the largest prime factor of n. We obtain several upper bounds on the number of solutions of congruences of the form n!+2 n -10(modq) and use these bounds to show that

lim supnP(n!+2n-1)/n(2π2+3)/18.

@article{JTNB_2005__17_3_859_0,
     author = {Florian Luca and Igor E. Shparlinski},
     title = {On the largest prime factor of $n!+ 2^n-1$},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {859--870},
     publisher = {Universit\'e Bordeaux 1},
     volume = {17},
     number = {3},
     year = {2005},
     doi = {10.5802/jtnb.524},
     mrnumber = {2212129},
     zbl = {1097.11006},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.524/}
}
Florian Luca; Igor E. Shparlinski. On the largest prime factor of $n!+ 2^n-1$. Journal de Théorie des Nombres de Bordeaux, Tome 17 (2005) no. 3, pp. 859-870. doi : 10.5802/jtnb.524. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.524/

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