For an integer we denote by the largest prime factor of . We obtain several upper bounds on the number of solutions of congruences of the form and use these bounds to show that
Pour un entier , notons le plus grand facteur premier de . Nous obtenons des majorations sur le nombre de solutions de congruences de la forme et nous utilisons ces bornes pour montrer que
DOI: 10.5802/jtnb.524
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@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/} }
TY - JOUR TI - On the largest prime factor of $n!+ 2^n-1$ JO - Journal de Théorie des Nombres de Bordeaux PY - 2005 DA - 2005/// SP - 859 EP - 870 VL - 17 IS - 3 PB - Université Bordeaux 1 UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.524/ UR - https://www.ams.org/mathscinet-getitem?mr=2212129 UR - https://zbmath.org/?q=an%3A1097.11006 UR - https://doi.org/10.5802/jtnb.524 DO - 10.5802/jtnb.524 LA - en ID - JTNB_2005__17_3_859_0 ER -
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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