$cyc$ means?Nirjhor wrote: $\displaystyle\sum_{\text{cyc}} \dfrac{ab+1}{(a+b)^2}$.
Search found 110 matches
Re: Minimize!
- Wed Mar 04, 2015 12:02 am
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO national 2014: junior 8
- Replies: 9
- Views: 7936
Re: BdMO national 2014: junior 8
badass0 wrote:
$EF^2$ এর মান কিভাবে $ \frac{5a^2}{8}$ হয়.
apply stewart's theorem in triangle $FVK$ .
- Tue Mar 03, 2015 11:45 pm
- Forum: Combinatorics
- Topic: AIME 1999
- Replies: 3
- Views: 3283
Re: AIME 1999
actually everyone will get the same answertanmoy wrote: I have got the same answer.
but the problem makes confusion because of its description.
- Tue Mar 03, 2015 7:35 pm
- Forum: Number Theory
- Topic: Divisibility
- Replies: 2
- Views: 2771
Re: Divisibility
$n^{k}-1=(n-1)(n^{k-1}+n^{k-2}+......+n^{0})$
so, we need to prove that $(n-1)$ divides $(n^{k-1}+n^{k-2}+......+n^{0})$
now,
$n^{k-1}\equiv 1(modn-1)$
$n^{k-2}\equiv 1(modn-1)$
.
.
.
$n^{0}\equiv 1(modn-1)$
so , $(n^{k-1}+n^{k-2}+......+n^{0})\equiv k\equiv 0(modn-1)$
so, we need to prove that $(n-1)$ divides $(n^{k-1}+n^{k-2}+......+n^{0})$
now,
$n^{k-1}\equiv 1(modn-1)$
$n^{k-2}\equiv 1(modn-1)$
.
.
.
$n^{0}\equiv 1(modn-1)$
so , $(n^{k-1}+n^{k-2}+......+n^{0})\equiv k\equiv 0(modn-1)$
- Tue Mar 03, 2015 7:26 pm
- Forum: Combinatorics
- Topic: AIME 1999
- Replies: 3
- Views: 3283
Re: AIME 1999
$\dfrac{40!}{2^{780}}$
- Tue Mar 03, 2015 12:04 am
- Forum: Number Theory
- Topic: Hungary 1995
- Replies: 2
- Views: 2732
Re: Hungary 1995
$(2,3,5,5)$ is a solution .
- Mon Mar 02, 2015 9:53 pm
- Forum: Secondary Level
- Topic: Bdmo 2013 secondary
- Replies: 3
- Views: 6274
Re: Bdmo 2013 secondary
$Strong$ $induction$ also gives a result .
- Mon Mar 02, 2015 7:29 pm
- Forum: Secondary Level
- Topic: Bdmo 2013 secondary
- Replies: 3
- Views: 6274
Bdmo 2013 secondary
There are $n$ cities in a country. Between any two cities there is at most one road. Suppose that the total
number of roads is $n$ . Prove that there is a city such that starting from there it is possible to come back to it
without ever travelling the same road twice .
number of roads is $n$ . Prove that there is a city such that starting from there it is possible to come back to it
without ever travelling the same road twice .
- Mon Mar 02, 2015 7:25 pm
- Forum: Number Theory
- Topic: USAMO 1972/1
- Replies: 2
- Views: 2621
Re: USAMO 1972/1
i think it is a very familiar problem
use PPF of a,b,c and work with the power of primes .
use PPF of a,b,c and work with the power of primes .
- Mon Mar 02, 2015 12:02 pm
- Forum: Number Theory
- Topic: Some GCD Problems
- Replies: 6
- Views: 6470
Re: Some GCD Problems
i thought $a^{2^{n}}=(a^{2})^{n}$ but you meant $a^{2^{n}}=a^{(2^{n})}$
sorry for the mistake .
sorry for the mistake .