Search found 153 matches

by Corei13
Sat Nov 05, 2011 3:14 pm
Forum: National Math Camp
Topic: solutions to camp exam problem
Replies: 28
Views: 8275

Re: solutions to camp exam problem

@Joty: I had only two to three hours to solve and latex all of them as I didn't know the date of exam. So, please inform if anything is not clear enough.

@Tiham: WLOG means Without Loss Of Generality.
by Corei13
Sat Nov 05, 2011 11:47 am
Forum: National Math Camp
Topic: solutions to camp exam problem
Replies: 28
Views: 8275

Re: solutions to camp exam problem

I only have my PDF file. So, I'm posting it here:
by Corei13
Fri Nov 04, 2011 6:59 pm
Forum: Introductions
Topic: Newbie From CA!!
Replies: 5
Views: 2740

Re: Newbie From CA!!

Welcome!
By the way, does CA mean California ?
by Corei13
Thu Nov 03, 2011 11:46 pm
Forum: Computer Science
Topic: gedit
Replies: 8
Views: 3269

Re: gedit

Your code is compiled in my pc without any problem. :-/

Try updating gcc: sudo apt-get install gcc
by Corei13
Thu Nov 03, 2011 8:37 pm
Forum: Computer Science
Topic: gedit
Replies: 8
Views: 3269

Re: gedit

Go to terminal and type: sudo apt-get install gedit-plugins After installing it go to Gedit > Edit > Preference > Plugins Then tick Embedded terminal. Now write a code, suppose something.c, when you need to compile it hit Ctrl+F9 and then enter gcc something.c . If compilation is OK, enter ./a.out t...
by Corei13
Tue Nov 01, 2011 10:41 pm
Forum: National Math Olympiad (BdMO)
Topic: Algebra: Inequalities
Replies: 14
Views: 4535

Re: Algebra: Inequalities

nafistiham wrote:ifile.it/zlct48/ebooksclub.org__Inequalities__A_Mathematical_Olympiad_Approach.pdf
এভাবে সর্বসম্মুখে কোন কপিরাইটেড জিনিসের ডাউনলোড লিঙ্ক পোস্ট করিস না। ;)
Use PM!
by Corei13
Tue Nov 01, 2011 6:16 pm
Forum: National Math Camp
Topic: UK 2008: Exercise 1.97 (BOMC)
Replies: 1
Views: 1094

Re: UK 2008: Exercise 1.97 (BOMC)

Let, $x^2 + y^2 + z^2 = A$, $xy + yz + zx = B$
$1 = (x^3 + y^3 + z^3 - 3xyz)^2 = (x+y+z)^2 (x^2 + y^2 + z^2 -xy -yz -zx)^2$
$=(A+2B)(A-B)^2 \leq \left ( \frac{(A+2B) + (A-B) + (A-B)}{3} \right)^3 = A^3$, by A.M-G.M with equality when $A+2B=A-B$ or $B=0$
SO, minimum of $x^2 + y^2 + z^2$ is $1$.
by Corei13
Sat Oct 29, 2011 12:54 am
Forum: International Mathematical Olympiad (IMO)
Topic: 2003 IMO Problem 5
Replies: 12
Views: 4911

Re: 2003 IMO Problem 5

\[ \left( \sum^n_{i, j = 1} |x_i - x_j | \right)^2 \leq \frac{2 (n^2 - 1)}{3} \sum^n_{i, j = 1} (x_i - x_j)^2 \] \[ \Longleftrightarrow \left( \sum_{1 \leq i < j \leq n} |x_i - x_j | \right)^2 \leq \frac{(n^2 - 1)}{3} \sum_{1 \leq i < j \leq n} (x_i - x_j)^2 \] \[ \Longleftrightarrow \left( \sum_{i ...
by Corei13
Mon Oct 17, 2011 2:06 pm
Forum: Combinatorics
Topic: China 1999
Replies: 0
Views: 1109

China 1999

Let, $A = \{1,2, \cdots n \}$ $\Im = \{(A_1,A_2,\cdots, A_n) | |A_i| \geq 2, |A_i \cap A_j| \leq 1 \text{ for } i\neq j \}$ And, \[ \forall \{i,j\}\subseteq A, \text{ } \forall (A_1,A_2,\cdots, A_n) \in \Im, \text{ }\exists u, 1 \leq u \leq n \text{ such that } \{i,j\} \subseteq A_u, \text{ }\{i,j\}...
by Corei13
Sun Oct 16, 2011 6:53 pm
Forum: Higher Secondary Level
Topic: ধারার সমস্যা
Replies: 7
Views: 2911

Re: ধারার সমস্যা

Hint :
$a_{4n+6} = a_{4n+7} - a_{4n+5}=a_{2n+3}-a_{2n+2}=a_{2n+1}=a_{n}$