## Search found 1007 matches

- Tue Nov 12, 2019 8:27 am
- Forum: International Mathematical Olympiad (IMO)
- Topic: IMO 2019/P3
- Replies:
**5** - Views:
**60119**

### Re: IMO 2019/P3

DAMN!!!!!!! This forum has got so dead... It needs a serious waking call... Maybe we should consider calling Thanos... to invade this forum. :twisted: Maybe then the "Avengers" (admins, moderators and former-active members) might turn their focus to this forum, again. :lol: (P.S: I don't know wheth...

- Tue Nov 12, 2019 8:25 am
- Forum: Combinatorics
- Topic: Turkey TST 2014
- Replies:
**7** - Views:
**67220**

### Re: Turkey TST 2014

Because there is no active member!Ragib Farhat Hasan wrote: ↑Tue Nov 05, 2019 12:57 amBTW, I wonder...

This problem was posted over 5 years ago.

And no one posted a solution to this problem in half a decade!!! WOW!!!

- Thu Aug 15, 2019 8:46 pm
- Forum: Asian Pacific Math Olympiad (APMO)
- Topic: APMO 2019 P5
- Replies:
**1** - Views:
**82773**

### APMO 2019 P5

Determine all the functions $f : \mathbb{R} \to \mathbb{R}$ such that

\[ f(x^2 + f(y)) = f(f(x)) + f(y^2) + 2f(xy) \]for all real numbers $x$ and $y$.

\[ f(x^2 + f(y)) = f(f(x)) + f(y^2) + 2f(xy) \]for all real numbers $x$ and $y$.

- Thu Aug 15, 2019 8:45 pm
- Forum: Asian Pacific Math Olympiad (APMO)
- Topic: APMO 2019 P4
- Replies:
**0** - Views:
**69800**

### APMO 2019 P4

Consider a $2018 \times 2019$ board with integers in each unit square. Two unit squares are said to be neighbours if they share a common edge. In each turn, you choose some unit squares. Then for each chosen unit square the average of all its neighbours is calculated. Finally, after these calculatio...

- Thu Aug 15, 2019 8:44 pm
- Forum: Asian Pacific Math Olympiad (APMO)
- Topic: APMO 2019 P3
- Replies:
**0** - Views:
**70373**

### APMO 2019 P3

Let $ABC$ be a scalene triangle with circumcircle $\Gamma$. Let $M$ be the midpoint of $BC$. A variable point $P$ is selected in the line segment $AM$. The circumcircles of triangles $BPM$ and $CPM$ intersect $\Gamma$ again at points $D$ and $E$, respectively. The lines $DP$ and $EP$ intersect (a se...

- Thu Aug 15, 2019 8:42 pm
- Forum: Asian Pacific Math Olympiad (APMO)
- Topic: APMO 2019 P2
- Replies:
**0** - Views:
**58276**

### APMO 2019 P2

Let $m$ be a fixed positive integer. The infinite sequence $\{a_n\}_{n\geq 1}$ is defined in the following way: $a_1$ is a positive integer, and for every integer $n\geq 1$ we have $$a_{n+1} = \begin{cases}a_n^2+2^m & \text{if } a_n< 2^m \\ a_n/2 &\text{if } a_n\geq 2^m\end{cases}$$For each $m$, det...

- Thu Aug 15, 2019 8:41 pm
- Forum: Asian Pacific Math Olympiad (APMO)
- Topic: APMO 2019 P1
- Replies:
**1** - Views:
**58257**

### APMO 2019 P1

Let $\mathbb{Z}^+$ be the set of positive integers. Determine all functions $f : \mathbb{Z}^+\to\mathbb{Z}^+$ such that $a^2+f(a)f(b)$ is divisible by $f(a)+b$ for all positive integers $a,b$.

- Thu May 16, 2019 10:40 am
- Forum: Physics
- Topic: BdPhO Regional (Dhaka-South) Higher Secondary 2019/2
- Replies:
**3** - Views:
**17404**

### Re: BdPhO Regional (Dhaka-South) Higher Secondary 2019/2

How did you draw this?

- Thu May 16, 2019 10:37 am
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National Secondary 2018:Full Solution
- Replies:
**4** - Views:
**15885**

### Re: BdMO National Secondary 2018:Full Solution

From the facebook page of Parallel Math School.SINAN EXPERT wrote: ↑Thu Apr 25, 2019 8:19 pmHow did you know about that?samiul_samin wrote: ↑Mon Feb 25, 2019 1:45 pmAll solution of the problems of BdMO National Secondary $2018$ are available here.

Made by Soyeb Pervez Jim

I mean this file is posted by Soyeb Pervez Jim.