## Search found 751 matches

Tue Jan 29, 2013 11:58 am
Forum: Social Lounge
Topic: May We Post Regional Problems?
Replies: 2
Views: 2788

### Re: May We Post Regional Problems?

Yep! Go ahead and post problems. Good luck at the BdMO.
Sun Dec 23, 2012 11:20 pm
Forum: News / Announcements
Topic: Posting BDMO 2013 problems: ZERO tolerance!
Replies: 7
Views: 10326

### Re: Posting BDMO 2013 problems: ZERO tolerance!

So another new year at BdMO forum and time to impose embargo. Please don't post divisional MO problems. Don't risk your life! Wed Aug 15, 2012 9:51 pm
Forum: Introductions
Topic: আমি জয়
Replies: 1
Views: 2663

### Re: আমি জয়

ফোরামে স্বাগতম। আশা করি নিয়মিত আলোচনায় যুক্ত থাকবে।
Mon Jul 16, 2012 1:44 pm
Forum: News / Announcements
Topic: IMO-2012 result of Bangladesh team
Replies: 4
Views: 4009

### Re: IMO-2012 result of Bangladesh team

Congratulations! I am planning to change the banner of the forum for a while to honor our heroes! Thu Jul 12, 2012 1:19 am
Topic: IMO 2012: Day 2 Problem 6
Replies: 1
Views: 3441

### IMO 2012: Day 2 Problem 6

Find all positive integers $n$ for which there exist non-negative integers $a_1,a_2,\cdots, a_n$ such that $\frac{1}{2^{a_1}}+\frac{1}{2^{a_2}}+\cdots+\frac{1}{2^{a_n}}=\frac{1}{3^{a_1}}+\frac{2}{3^{a_2}}+\cdots+\frac{n}{3^{a_n}}=1$
Thu Jul 12, 2012 1:02 am
Topic: IMO 2012: Day 2 Problem 5
Replies: 5
Views: 5019

### IMO 2012: Day 2 Problem 5

Let $ABC$ be a triangle with $\angle {ACB}=90^0$ and let $D$ be the foot of the altitude from $C$. Let $X$ be a point in the interior of the segment $CD$. Let $K$ be the point on the segment $AX$ such that $BK=BC$. Similarly, let $L$ be the point on the segment $BX$ such that $AL=AC$. Let $M$ be the...
Wed Jul 11, 2012 11:29 pm
Topic: IMO 2012: Day 2 Problem 4
Replies: 4
Views: 5010

### IMO 2012: Day 2 Problem 4

Find all functions $f:\mathbb{Z}\rightarrow \mathbb{Z}$, such that for all $a+b+c=0$ holds:
$f(a)^2+f(b)^2+f(c)^2=2f(a)f(b)+2f(b)f(c)+2f(c)f(a).$
Tue Jul 10, 2012 11:56 pm
Topic: IMO 2012: Day 1 Problem 2
Replies: 12
Views: 9679

### Re: IMO 2012: Day 1 Problem 2

It seems that there is no $a_1$ thanks for pointing out. Tue Jul 10, 2012 11:51 pm
Topic: IMO 2012: Day 1 Problem 3
Replies: 1
Views: 3634

### IMO 2012: Day 1 Problem 3

The liar's guessing game is a game played between two players $A$ and $B$. The rules of the game depend on two positive integers $k$ and $n$ which are known to both players. At the start of the game $A$ chooses integers $x$ and $N$ with $1 \le x \le N.$ Player $A$ keeps $x$ secret, and truthfully te...
Tue Jul 10, 2012 11:31 pm
Let $n \ge 3$ be an integer, and let $a_2, a_3, \ldots , a_n$ be positive real numbers such that $a_2\cdots a_n = 1.$
Prove that $(1+a_2)^2(1+a_3)^3\cdots (1+a_n)^n > n^n$