Problem 1. Let n be a positive integer and let a1,a2,a3,...,ak ( k≥ 2) be distinct integer in the set { 1,2,...,n} such that n divides ai(ai+1-1) for i = 1,2,...,k-1. Prove that n does not divide ak(a1-1).
Problem 2. Let ABC be a triangle with circumcenter O. The points P and Q are interior points of the sides CA and AB respectively. Let K,L and M be the midpoints of the segments BP,CQ and PQ. respectively, and let Γ be the circle passing through K,L and M. Suppose that the line PQ is tangent to the circle Γ. Prove that OP = OQ.
Problem 3. Suppose that s1,s2,s3, ... is a strictly increasing sequence of positive integers such that the sub-sequences ss_{1},ss_{2},ss_{3}, ... and ss_{1+1},ss_{2+1},ss_{3+1}, ... are both arithmetic progressions. Prove that the sequence s1,s2,s3, ... is itself an arithmetic progression.
Thursday, July 16, 2009
Thursday, June 11, 2009
Your chance to learn many things from SEALNet!
Project Cambodia (Arts)
When: Monday 10 August 2009 – Tuesday 25 August 2009
Location: Phnom Penh, Cambodia
Project Cambodia 2009 (PC09) aims to help renew interest in traditional Cambodian performing arts through the production of two outreach concerts in Phnom Penh. PC09, partnered with Cambodian Living Arts, hopes to innovate the presentation of traditional Cambodian dance and storytelling by incorporating elements of other contemporary performing arts styles. In creating a very dynamic program, the production will particularly appeal to youth and overall provide greater access to exciting arts for the wider community. We envision the establishment of the first annual youth concert in Phnom Penh and celebration of traditional Cambodian arts, which is independently owned by Cambodian youth of diverse social backgrounds.
Objectives
The main objective of PC09 is to identify, encourage, and support Cambodian youth by creating an opportunity for these students to gain leadership and personal development skills and experience.
• Empower youth and give them the tools to positively impact their community and culture.
• Promote the development of performing arts by aiming to provide a solid platform for young Cambodian artists to experiment and expose their talents.
• To equip Cambodian youth leaders with skills to engage in their society in any given discipline.
Requirements
• Students of grade 11 or 12 in any high schools or freshman in any universities.
• Proper level of English proficiency.
• Strongly interested in our project and volunteer to distribute the project.
If you are interested in this program and want to apply, please click here!
Sorry for inconvinience, since we have some problems with the survey website, please send all the answers to our mail group_cmg@yahoo.com if you want to apply. Thanks for your cooperation!
Just want to confirm, for question 4 and 5, you should write between 200 and 250 words.
Note : Deadline is 28th June 2009 by 12:00am
Tuesday, May 12, 2009
A cool book you should read!
Friday, May 1, 2009
The 36th Ship for South East Asian Youth Program 2009
Recently, there is a program called Ship for South East Asian Youth Program ( SSEAYP ) which will be held from 27 October 2009 until 17 December 2009. This program is a great opportunity for all Cambodian youth to show their ability and represent their country in global stage. Usually, successive contestants will be given a chance to visit 4 countries in South East Asia and Japan by ship in order to show their tradition, culture and ability. I am sure this is your turning point if you take part in this program!
How many contestants will be selected?
1 leader ( selected by ministry of education, youth and sport )
2 skilled artists ( 1 male and 1 female )
26 contestants ( 13 males and 13 females )
If you are interested in this program, please see if you complete the requirement as following:
Have good health and between the age of 18 and 30 ( counting until 1st April, 2009 )
Have good knowledge in English ( both speaking and Writing)
Have good characteristics ( friendly and have good morality )
Love art and have awareness of ASEAN, environment problem and education
Have good discipline and responsibility
Can support to buy personal insurance during the program
Can support to buy using material, souvenir and passport
Have ability and enough time to join the training lasting about 2 months prior to the departure
The application form can be bought at Youth Department which is near Paññasastra University of Cambodia ( south campus ).
Deadline : 29th May 2009
How many contestants will be selected?
1 leader ( selected by ministry of education, youth and sport )
2 skilled artists ( 1 male and 1 female )
26 contestants ( 13 males and 13 females )
If you are interested in this program, please see if you complete the requirement as following:
Have good health and between the age of 18 and 30 ( counting until 1st April, 2009 )
Have good knowledge in English ( both speaking and Writing)
Have good characteristics ( friendly and have good morality )
Love art and have awareness of ASEAN, environment problem and education
Have good discipline and responsibility
Can support to buy personal insurance during the program
Can support to buy using material, souvenir and passport
Have ability and enough time to join the training lasting about 2 months prior to the departure
The application form can be bought at Youth Department which is near Paññasastra University of Cambodia ( south campus ).
Deadline : 29th May 2009
Sunday, April 12, 2009
Happy Khmer New Year 2009
I would like to send this greeting card to all our buddies and members here.
Tuesday, February 10, 2009
Monday, February 9, 2009
Methematica- A math_computing free contest. anyone can join!
Important : Registered as soon as possible. 13Feb is the deadLine.
It is one of the onlie mathematic_computing competition. I'm not sure, but base on reading, Anyone can register for it and take award if they pass regardless of where , how old you are.
Some exam question can be found in here. Most of the problems might need to use computer programming. http://felicity.iiit.ac.in/~math/WLogin/Handle.py/Handle?RequestedPage=ArchivesPage
To register , visit this page.
P.S I have created my own team. If any one wanna join, can.
My team is Jupiter (I'm alone, not yet have member). (Find it in Registered team)
Tuesday, February 3, 2009
Mathematical Excalibur from Hong Kong
Mathematical Excalibur is a mathematic magazine that publish after The 35th International Mathematical Olympiad was held in Hong Kong. This magazine was written in English and Traditional Chinese by Hong Kong University of Science and Technology, Department of Mathematics.
Anyway you can receive material for new issue, just create your individual subscription to author of this magazine. You can download it here: http://www.math.ust.hk/excalibur/
Anyway you can receive material for new issue, just create your individual subscription to author of this magazine. You can download it here: http://www.math.ust.hk/excalibur/
Saturday, January 17, 2009
Dear all members here!
Dear all member here! I'm Piseth, the last senior member of CMG. I'm really pleased that Xiao Wei invite me to contribute with CMG. Hrm... my English is not good so I can't write too much. I have something want to ask. CMG has a Khmer blog, right? Why we don't update it?
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