Search found 1004 matches

by samiul_samin
Thu Aug 15, 2019 8:46 pm
Forum: Asian Pacific Math Olympiad (APMO)
Topic: APMO 2019 P5
Replies: 0
Views: 329

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 $y$.
by samiul_samin
Thu Aug 15, 2019 8:45 pm
Forum: Asian Pacific Math Olympiad (APMO)
Topic: APMO 2019 P4
Replies: 0
Views: 232

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...
by samiul_samin
Thu Aug 15, 2019 8:44 pm
Forum: Asian Pacific Math Olympiad (APMO)
Topic: APMO 2019 P3
Replies: 0
Views: 237

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...
by samiul_samin
Thu Aug 15, 2019 8:42 pm
Forum: Asian Pacific Math Olympiad (APMO)
Topic: APMO 2019 P2
Replies: 0
Views: 240

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...
by samiul_samin
Thu Aug 15, 2019 8:41 pm
Forum: Asian Pacific Math Olympiad (APMO)
Topic: APMO 2019 P1
Replies: 0
Views: 244

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 $a,b$.
by samiul_samin
Thu May 16, 2019 10:40 am
Forum: Physics
Topic: BdPhO Regional (Dhaka-South) Higher Secondary 2019/2
Replies: 3
Views: 850

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

SINAN EXPERT wrote:
Fri Apr 26, 2019 8:55 pm
Solution:
BdPhO Regional (Dhaka-South) Higher Secondary 2019(3S).png
How did you draw this?
by samiul_samin
Thu May 16, 2019 10:37 am
Forum: National Math Olympiad (BdMO)
Topic: BdMO National Secondary 2018:Full Solution
Replies: 2
Views: 1044

Re: BdMO National Secondary 2018:Full Solution

SINAN EXPERT wrote:
Thu Apr 25, 2019 8:19 pm
samiul_samin wrote:
Mon Feb 25, 2019 1:45 pm
All solution of the problems of BdMO National Secondary $2018$ are available here.

Made by Soyeb Pervez Jim
How did you know about that?
From the facebook page of Parallel Math School.
I mean this file is posted by Soyeb Pervez Jim.
by samiul_samin
Thu May 16, 2019 10:36 am
Forum: Algebra
Topic: 0^0=1!
Replies: 5
Views: 866

Re: 0^0=1!

SINAN EXPERT wrote:
Wed Apr 24, 2019 4:57 pm
Yeah, that's not any joke! I'm really gonna prove that!
We know, $2^6=64$
Again, $2^6=(2+0)^6=6_{C_0}2^60^0+6_{C_1}2^50^1+6_{C_2}2^40^2+...=64*0^0$ $⇒64=64*0^0$
Which is a clear proof of $0^0=1$.
True to say, I haven't found any mistake here. :D
Why $64\times 0^0=64$?
by samiul_samin
Wed Apr 10, 2019 10:18 am
Forum: National Math Olympiad (BdMO)
Topic: BdMO National Higher Secondary 2019/9
Replies: 2
Views: 643

Re: BdMO National Higher Secondary 2019/9

No need to draw a figure?
by samiul_samin
Wed Apr 10, 2019 10:17 am
Forum: Combinatorics
Topic: how to solve this?
Replies: 2
Views: 698

Re: how to solve this?

Formula$\dbinom{n-1}{k-1}$
You can get a link of nice book
Here