On the largest prime factor of
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
Journal de Théorie des Nombres de Bordeaux (2005)
- Volume: 17, Issue: 3, page 859-870
- ISSN: 1246-7405
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topLuca, Florian, and Shparlinski, Igor E.. "On the largest prime factor of $n!+ 2^n-1$." Journal de Théorie des Nombres de Bordeaux 17.3 (2005): 859-870. <http://eudml.org/doc/249430>.
@article{Luca2005,
abstract = {For an integer $n\ge 2$ 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 $n!+2^n - 1 \equiv 0 \hspace\{4.44443pt\}(\@mod \; q)$ and use these bounds to show that\[\limsup \_\{n \rightarrow \infty \}P(n!+2^n - 1)/n \ge (2 \pi ^2 + 3)/18. \]},
affiliation = {Instituto de Matemáticas Universidad Nacional Autónoma de México C.P. 58089, Morelia, Michoacán, México; Macquarie University Sydney, NSW 2109, Australia},
author = {Luca, Florian, Shparlinski, Igor E.},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {largest prime factor; number of distinct prime factors; number of solutions of congruences},
language = {eng},
number = {3},
pages = {859-870},
publisher = {Université Bordeaux 1},
title = {On the largest prime factor of $n!+ 2^n-1$},
url = {http://eudml.org/doc/249430},
volume = {17},
year = {2005},
}
TY - JOUR
AU - Luca, Florian
AU - Shparlinski, Igor E.
TI - On the largest prime factor of $n!+ 2^n-1$
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2005
PB - Université Bordeaux 1
VL - 17
IS - 3
SP - 859
EP - 870
AB - For an integer $n\ge 2$ 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 $n!+2^n - 1 \equiv 0 \hspace{4.44443pt}(\@mod \; q)$ and use these bounds to show that\[\limsup _{n \rightarrow \infty }P(n!+2^n - 1)/n \ge (2 \pi ^2 + 3)/18. \]
LA - eng
KW - largest prime factor; number of distinct prime factors; number of solutions of congruences
UR - http://eudml.org/doc/249430
ER -
References
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