## Search found 110 matches

Wed Mar 04, 2015 12:37 am
Forum: Algebra
Topic: Minimize!
Replies: 4
Views: 1978

### Re: Minimize!

Nirjhor wrote: $\displaystyle\sum_{\text{cyc}} \dfrac{ab+1}{(a+b)^2}$.
$cyc$ means? Wed Mar 04, 2015 12:02 am
Topic: BdMO national 2014: junior 8
Replies: 9
Views: 4158

### Re: BdMO national 2014: junior 8

$EF^2$ 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: 1527

### Re: AIME 1999

tanmoy wrote: I have got the same answer. actually everyone will get 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: 1256

### 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 , $(n^{k-1}+n^{k-2}+......+n^{0})\equiv k\equiv 0(modn-1)$
Tue Mar 03, 2015 7:26 pm
Forum: Combinatorics
Topic: AIME 1999
Replies: 3
Views: 1527

### Re: AIME 1999

$\dfrac{40!}{2^{780}}$
Tue Mar 03, 2015 12:04 am
Forum: Number Theory
Topic: Hungary 1995
Replies: 2
Views: 1213

### 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: 3090

### 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: 3090

### 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 .
Mon Mar 02, 2015 7:25 pm
Forum: Number Theory
Topic: USAMO 1972/1
Replies: 2
Views: 1161

### 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 .
Mon Mar 02, 2015 12:02 pm
Forum: Number Theory
Topic: Some GCD Problems
Replies: 6
Views: 2029

### 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 . 