$cyc$ 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:
**4900**

### 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:
**1876**

### 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:
**1544**

### 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:
**1876**

### Re: AIME 1999

$\dfrac{40!}{2^{780}}$

- Tue Mar 03, 2015 12:04 am
- Forum: Number Theory
- Topic: Hungary 1995
- Replies:
**2** - Views:
**1514**

### 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:
**3495**

### 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:
**3495**

### 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:
**1437**

### 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:
**2603**

### 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 .