be an odd integer. Prove that there exists a prime number 
such that![\[
p \mid 2^{\varphi(n)} - 1 \quad \text{but} \quad p \nmid n.
\]](http://latex.artofproblemsolving.com/3/5/1/3514b64ecd5f7b2586d5bfeae59b7c9504d5b455.png)
be non-negative real numbers such that 
Prove that
be real numbers satisfying 
. Find the maximum value of![\[P = \dfrac{a(b+c)}{a^2+2bc+3} + \dfrac{b(a+c) }{b^2+2ca +3 } + \dfrac{c(a+b)}{c^2+2ab+3}.\]](http://latex.artofproblemsolving.com/7/b/2/7b2ec0a87ca05d3cb29da888a4dfa73e10f238f8.png)
and 
. Prove that 
Y by Kayak, WizardMath, adityaguharoy, IMO2019, lifeisgood03, e_plus_pi, shinichiman, Mathisfun04, zuss77, tauros, Wizard_32, pheonix002, Carpemath, Vrangr, Devastator, thunderz28, brokendiamond, Samsuman, khan.academy, Iamawesome1, MathStudent2002, rzlng, lkarhat, XMaths, fry8, TheCoolDinosuar, Centralorbit, AlastorMoody, MathPassionForever, NoDealsHere, Hexagrammum16, IMO2018, look4pilot, Ultroid999OCPN, Euler1728, mihaig, mathleticguyyy, TuZo, Math-wiz, Combi1234, LIPENGTAO, Feridimo, aops29, aa1024, RudraRockstar, magicarrow, amar_04, JosefSvejk, Anajar, HWenslawski, Adventure10, Mango247, aidan0626
I should have created this topic long ago.
Olympiad Archive (AoPS Wiki)
Since adding links to the tables in the Wiki page might not be easy for everyone, you can post the link and the description of the contest that you want to be added under this topic (you don't need to create the whole list again; just paste your link here and I'll take care of it). I will update the page once in a while to add the new links/fix the broken ones.
I have also created a Dropbox folder for this purpose. If you have the problems of olympiads of some countries (except the ones that are already present on AoPS Contests page) and want to share it with us, please
Dropbox links: to upload files in the Dropbox folder, use this link and to view the uploaded files, use this link.
Thank you!
EDIT. Updated. I will create the Wiki page as soon as we get 50 competitions in the list.
Olympiad Archive (AoPS Wiki)
Since adding links to the tables in the Wiki page might not be easy for everyone, you can post the link and the description of the contest that you want to be added under this topic (you don't need to create the whole list again; just paste your link here and I'll take care of it). I will update the page once in a while to add the new links/fix the broken ones.
I have also created a Dropbox folder for this purpose. If you have the problems of olympiads of some countries (except the ones that are already present on AoPS Contests page) and want to share it with us, please
- Compress all your files into one ZIP/RAR/7z file.
- Rename the file in the following format:
[Country]_[Competition Name]_[Competition Years]_[With/Without Solutions]_[Language]
- For instance, if you want to upload the problems (but not solutions) of the second round national olympiad of Iran between the years 2010 to 2017 and in Farsi, the name of the file that you upload must be:
Iran_Second Round_2010-2017_Without Solutions_Farsi
Dropbox links: to upload files in the Dropbox folder, use this link and to view the uploaded files, use this link.
Thank you!
EDIT. Updated. I will create the Wiki page as soon as we get 50 competitions in the list.
This post has been edited 5 times. Last edited by Amir Hossein, Jun 20, 2018, 9:37 AM
![$\begin{tabular}{c|c|c|c|c}Country & Abbreviation & Name & Link & Languages \\ \hline
International & IOL & International Linguistics Olympiad & [url]http://www.ioling.org/problems/[/url] & Multiple \\
Australia & OzCLO & The Australian Computational and Linguistics Olympiad & [url]http://ozclo.org.au/past-problems/[/url] & English \\
Brazil & OBL & Olimpiada Brasileira de Linguistica & [url]http://www.obling.org/problemas[/url] & Portuguese \\
Estonia & - & Lingvistikaolümpiaad & https://www.teaduskool.ut.ee/et/olumpiaadid/lingvistikaolumpiaadi-arhiiv & Estonian \\
USA & NACLO & North American Computational Linguistics Olympiad & [url]http://nacloweb.org/practice.php[/url] & English \\
\end{tabular}$](http://latex.artofproblemsolving.com/1/c/a/1ca182e369b72518c6454bde59378b43a3192567.png)
