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

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.

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.

DOI: 10.5802/jtnb.524
Florian Luca 1; Igor E. Shparlinski 2

1 Instituto de Matemáticas Universidad Nacional Autónoma de México C.P. 58089, Morelia, Michoacán, México
2 Macquarie University Sydney, NSW 2109, Australia
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Florian Luca; Igor E. Shparlinski. On the largest prime factor of $n!+ 2^n-1$. Journal de théorie des nombres de Bordeaux, Volume 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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