Search found 550 matches
- Tue Feb 05, 2013 11:54 pm
- Forum: Higher Secondary Level
- Topic: Secondary and Higher Secondary Marathon
- Replies: 128
- Views: 299298
Re: Secondary and Higher Secondary Marathon
Firstly if $x,y$ are both non-negative,then we can do the following: $n^2\equiv 0(mod 4)$ here.And also $3\equiv -1(mod 4)$ and $7\equiv -1(mod 4)$. So one of $x,y$ is odd and the other is even. Let $x=2a,y=2b+1$. Then $7^{2b+1}=n^2-3^{2a}=(n+3^{a})(n-3^{a})$. Now we can assume that $n+3^{a}=7^{p},n...
- Tue Feb 05, 2013 11:16 pm
- Forum: Higher Secondary Level
- Topic: Secondary and Higher Secondary Marathon
- Replies: 128
- Views: 299298
Re: Secondary and Higher Secondary Marathon
I have a confusion here. Can $x,y$ be negative?FahimFerdous wrote:Problem 38:
$3^x+7^y=n^2$
how many integer solutions for $(x,y)$ are there?
- Thu Jan 31, 2013 6:41 pm
- Forum: International Mathematical Olympiad (IMO)
- Topic: IMO Marathon
- Replies: 184
- Views: 113903
Re: IMO Marathon
Sorry, Edited now. The source I used had a typo. Sorry for the inconvenience.
- Thu Jan 31, 2013 10:32 am
- Forum: Higher Secondary Level
- Topic: Secondary and Higher Secondary Marathon
- Replies: 128
- Views: 299298
Re: Secondary and Higher Secondary Marathon
Problem $\boxed{35}$ Find all $5$-digit natural numbers $n$ such that $n^2$ ends in all the same as $n$. Source: Book 'Olympiad Somogro'(Bangla) Can you please tell us what you meant by all the same as $n$? If it meas only the last digit,then the last digit of $n$ will be any of $0,1,5,6$. The rema...
- Wed Jan 30, 2013 10:29 pm
- Forum: International Mathematical Olympiad (IMO)
- Topic: IMO Marathon
- Replies: 184
- Views: 113903
Re: IMO Marathon
Problem $\boxed {27}$:
Find all values for a real parameter $\alpha$ for which there exists exactly one function $f:\mathbb {R}\rightarrow \mathbb {R}$ satisfying
$f(x^2+y+f(y))=f(x)^2+\alpha \cdot y$
Vietnam-2005
Find all values for a real parameter $\alpha$ for which there exists exactly one function $f:\mathbb {R}\rightarrow \mathbb {R}$ satisfying
$f(x^2+y+f(y))=f(x)^2+\alpha \cdot y$
Vietnam-2005
- Wed Jan 30, 2013 12:52 pm
- Forum: Secondary Level
- Topic: Prove it
- Replies: 8
- Views: 5273
Re: Prove it
Did you wanted to tell that if $d|a_1,d|a_2,...,d|a_n$ then $d|c_1a_1 + c_2a_2+...+c_na_n$ ?famim2011 wrote:If d [ a u d | a 2 , . . .,d\a n , then d \
(ciOi + c 2 a 2 + • • • + c n a n )
for any integers c\, c 2 , . . • ,
- Tue Jan 29, 2013 9:30 pm
- Forum: Secondary Level
- Topic: Number theory
- Replies: 3
- Views: 2918
Re: Number theory
the largest common divisor of $n$ and $0$ is $0$?*Mahi* wrote:$(n,0)=0$ .
- Thu Jan 24, 2013 10:58 pm
- Forum: Higher Secondary Level
- Topic: Some Last year Divisional Problems
- Replies: 13
- Views: 10442
Re: Some Last year Divisional Problems
Firstly problem $6$ has a wrong statement. For problem $2$ , The diameter of the circle is the side of the squares(think why),and they have the same area. For problem $2$ , Remember that if the prime factorization of $n$ is $p_{1}^{a_{1}}\times p_{2}^{a_{2}}\times ...\times p_{k}^{a_{k}}$ then the n...
- Wed Jan 23, 2013 10:36 pm
- Forum: International Mathematical Olympiad (IMO)
- Topic: IMO Marathon
- Replies: 184
- Views: 113903
Re: IMO Marathon
Problem $\boxed {23}$:
Let $a,b,c$ be positive real numbers such that $a+b+c=1$. Prove that
$\displaystyle\frac{ab}{\sqrt {ab+bc}}+\displaystyle\frac{bc}{\sqrt {bc+ca}}+\displaystyle\frac{ca}{\sqrt {ca+ab}} \leq \displaystyle\frac{1}{\sqrt {2}}$
Source: Chinese MO 2006
Let $a,b,c$ be positive real numbers such that $a+b+c=1$. Prove that
$\displaystyle\frac{ab}{\sqrt {ab+bc}}+\displaystyle\frac{bc}{\sqrt {bc+ca}}+\displaystyle\frac{ca}{\sqrt {ca+ab}} \leq \displaystyle\frac{1}{\sqrt {2}}$
Source: Chinese MO 2006
- Mon Jan 21, 2013 10:27 pm
- Forum: Secondary Level
- Topic: নিউরনে অনুরণন থেকে...
- Replies: 6
- Views: 15646
Re: নিউরনে অনুরণন থেকে...
Here is a tutorial on LTE. I hope you will find it useful.sakib.creza wrote:Adib Bhai, what's LTE. And please give detailed solution.