Search found 181 matches

by ahmedittihad
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.
by ahmedittihad
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

protaya das wrote:
Sun Dec 10, 2017 3:34 pm
8-) plz say what is perpendicullar lemma. i am protaya das. a winner of national bdmo on 2017 from junior category
Hello Protya Das, winner of bdmo 2017, the perpendicular lemma is this
by ahmedittihad
Sat Feb 17, 2018 1:41 am
Forum: Combinatorics
Topic: বিয়ে
Replies: 6
Views: 8209

Re: বিয়ে

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