Search found 592 matches
- Fri Aug 21, 2015 11:16 pm
- Forum: National Math Camp
- Topic: Online Number Theory Camp, 2015
- Replies: 1
- Views: 5912
Online Number Theory Camp, 2015
Well, the first online camp of this year is on. I will post any updates here. Stay tuned if you are a participant. If you don't have an account here, create one. I will post the syllabus and text books later. For now, know that, there will be a gap for you to study the materials or text books. Then ...
- Fri Aug 21, 2015 1:50 am
- Forum: Combinatorics
- Topic: Combinatorial Identity
- Replies: 0
- Views: 1932
Combinatorial Identity
Prove the following:
\[\sum_{k=0}^n\binom{2k}k\binom{2n-2k}{n-k}=4^n\]
\[\sum_{k=0}^n\binom{2k}k\binom{2n-2k}{n-k}=4^n\]
- Thu Aug 20, 2015 1:03 pm
- Forum: Asian Pacific Math Olympiad (APMO)
- Topic: Generalization of APMO 2015, problem 4
- Replies: 0
- Views: 2353
Generalization of APMO 2015, problem 4
Can this problem from APMO 2015 be generalized for any $k\leq2n$? Which means: Prove or disprove: In a plane, there are $2n$ distinct lines where $n$ is a positive integer. Among them, $n$ lines are colored blue and $n$ lines are colored red and no two lines are parallel. Let $\mathcal{B}$($\mathcal...
- Thu Aug 20, 2015 1:02 pm
- Forum: Asian Pacific Math Olympiad (APMO)
- Topic: APMO 2015, problem 4
- Replies: 1
- Views: 6999
APMO 2015, problem 4
In a plane, there are $2n$ distinct lines where $n$ is a positive integer. Among them, $n$ lines are colored blue and $n$ lines are colored red and no two lines are parallel. Let $\mathcal{B}$($\mathcal{R}$) be the set of all points that lie on at least one blue(red) line. Prove that, there exists a...
- Tue Aug 11, 2015 2:16 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO 2015 Problems
- Replies: 1
- Views: 2359
BdMO 2015 Problems
If anyone has the problemsets of BdMO 2015(national specially), please upload here.
- Sun Aug 09, 2015 9:42 pm
- Forum: Combinatorics
- Topic: Initial order of first $n$ numbers
- Replies: 1
- Views: 4707
Initial order of first $n$ numbers
The integers $1,...,n$ are arranged in any order. In one step any two neighboring integers may be interchanged. Prove that the initial order can never be reached after an odd number of steps.
- Sun Aug 09, 2015 8:13 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO Problem Sets of Previous Years
- Replies: 1
- Views: 4590
BdMO Problem Sets of Previous Years
If anyone has problem sets of national olympiads of previous years(except $2011$ and $2012$), please upload here.
- Mon Jul 20, 2015 12:57 pm
- Forum: Number Theory
- Topic: Factorial divisible by Mersenn Numbers
- Replies: 1
- Views: 2720
Factorial divisible by Mersenn Numbers
Find all positive integer $n$ so that $n!$ is divisible by $2^n-1$.
- Thu Apr 09, 2015 5:36 pm
- Forum: Number Theory
- Topic: IMO NT Compilation
- Replies: 2
- Views: 3567
Re: IMO NT Compilation
Yeah, whenever you find something wrong, just post it here so people can see. Because editing the doc is pointless now.
Re: পাকা চুল
খুবই জরুরী একটি প্রশ্ন। আমার কয়টা চুল পাকছে কেন জানি।