## Search found 181 matches

- Sat Feb 17, 2018 1:58 am
- Forum: Social Lounge
- Topic: Chat thread
- Replies:
**53** - Views:
**44379**

### Re: Chat thread

Well, if you want to open a thread, do it? People don't stay active anyway.

- Sat Feb 17, 2018 1:51 am
- Forum: National Math Olympiad (BdMO)
- Topic: BDMO NATIONAL Junior 2016/04
- Replies:
**8** - Views:
**3048**

### Re: BDMO NATIONAL Junior 2016/04

Hello Protya Das, winner of bdmo 2017, the perpendicular lemma is thisprotaya das wrote: ↑Sun Dec 10, 2017 3:34 pmplz say what is perpendicullar lemma. i am protaya das. a winner of national bdmo on 2017 from junior category

- Sat Feb 17, 2018 1:41 am
- Forum: Combinatorics
- Topic: বিয়ে
- Replies:
**6** - Views:
**8209**

### Re: বিয়ে

Yes, yes I am proud of my knowledge of marriage procedures.SN.Pushpita wrote: ↑Thu Feb 15, 2018 1:38 pmAre you proud of your knowledge regarding Hall's Marriage Lemma?:p

- Tue Feb 06, 2018 10:08 pm
- Forum: Junior Level
- Topic: The Chinese Remainder Theorem
- Replies:
**1** - Views:
**1325**

### Re: The Chinese Remainder Theorem

Sorry for the late reply, your post isn't very clear. Can you write it clearly again please?

- Tue Feb 06, 2018 10:05 pm
- Forum: Site Support
- Topic: Help me please
- Replies:
**1** - Views:
**7284**

### Re: Help me please

The $LaTeX$ was ruined. It's alright now.

- Tue Feb 06, 2018 10:02 pm
- Forum: Number Theory
- Topic: Integer
- Replies:
**1** - Views:
**3725**

### Re: Integer

There exists another thread on this problem. Please delete this one.

- Tue Feb 06, 2018 10:01 pm
- Forum: Number Theory
- Topic: Integer
- Replies:
**1** - Views:
**3842**

### Re: Integer

If $ab-1 | b^2+a$ then, $ab-1 | b(b^2+a)-(ab-1)$. So, $ab-1 | b^3+a$. Now this is IMO 1994 P4.

See the link for solution. https://artofproblemsolving.com/community/c6h2023p6413

See the link for solution. https://artofproblemsolving.com/community/c6h2023p6413

- Tue Feb 06, 2018 1:52 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BDMO 2017 National round Secondary 1
- Replies:
**19** - Views:
**7792**

### Re: BDMO 2017 National round Secondary 1

(a) Bangladesh wins the series in $3$ matches iff they win all $3$ of the games. And the probability of that is $\dfrac{1}{8}$. (b) Out of the $16$ cases of a $4$ length binary string, Only 3 of them satisfy (WWLW, WLWW,LWWW). So the probability here is $\dfrac{3}{16}. (b) Probability of winning th...

- Tue Feb 06, 2018 1:40 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BDMO 2017 National round Secondary 3
- Replies:
**6** - Views:
**2267**

### Re: BDMO 2017 National round Secondary 3

Stuck at last step. Please help if anyone can solve Let $r_1$ and $r_2$ be the roots of the equation $x^2+3x-1=0$. So, we can write: $r_1+r_2=\frac{-b}{a}=\frac{-3}{1}=-3$... 1|) $r_1r_2=\frac{c}{a}=\frac{-1}{1}=-1$... (2) We can write the quartic equation in this way: $x^4+dx^3+ax^2+bx+c=0$ where,...

- Tue Feb 06, 2018 1:36 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BDMO 2017 National round Secondary 3
- Replies:
**6** - Views:
**2267**

### Re: BDMO 2017 National round Secondary 3

I'll just give my solution. The polynomial $x^2+3x-1$ divides $x^4+ax^2+bx+c$. So, there exists a polynomial $P(x)$ such that $x^2+3x-1 \times P(x) = x^4+ax^2+bx+c$. Obviously, $P(x)$ is a monic quadratic. Let $P(x)= x^2+mx+n$. Then, $x^2+3x-1 \times P(x) = (x^2+3x-1) \times (x^2+mx+n) = x^4+(m+3)x^...