Search found 24 matches
- Tue Nov 06, 2012 1:03 am
- Forum: National Math Camp
- Topic: Bangladesh TST(Team selection test) 2011 Exam 4 Problem 1
- Replies: 4
- Views: 5096
Re: Bangladesh TST(Team selection test) 2011 Exam 4 Problem
Is it all $n$ which are divisible by $3$ ?
- Tue Oct 11, 2011 10:59 pm
- Forum: Combinatorics
- Topic: COMBINATORICS MARATHON: SEASON 2
- Replies: 22
- Views: 13416
Re: COMBINATORICS MARATHON: SEASON 2
I just found two simple recursions. Those recursions can be solved either using generating functions or using other algebra stuffs. are your equations for odd $n$ and even $n$,is it a three term recurrence?could you give your recursions,i want to check with my one.Iam not so sure about my solution....
- Tue Oct 11, 2011 1:18 pm
- Forum: Combinatorics
- Topic: sub sequences
- Replies: 0
- Views: 1813
sub sequences
The elements of the set $H$ are finite sequences whose elements are from {$1,2,3$}. Suppose that no element of $H$ is a subsequence of any other element of $H$. Show that $H$ is finite
- Tue Oct 11, 2011 12:32 am
- Forum: Combinatorics
- Topic: PIRATES
- Replies: 4
- Views: 3631
Re: PIRATES
you can get the answer considering the remainders of the pirates gold coins and computing between them.
- Tue Oct 11, 2011 12:28 am
- Forum: Combinatorics
- Topic: COMBINATORICS MARATHON: SEASON 2
- Replies: 22
- Views: 13416
Re: COMBINATORICS MARATHON: SEASON 2
Did he solve it by using generating functions?
- Mon Oct 10, 2011 9:11 pm
- Forum: Combinatorics
- Topic: coloring a 100x100 square with four colors
- Replies: 0
- Views: 1880
coloring a 100x100 square with four colors
Suppose that we color each point in a $100*100$ array with $4$ colors red,green,blue, and purple such that there are $25$ points of each color in each row and in each column. Prove that there exist $2$ rows and $2$ columns such that their $4$ intersections points are all different colors.
- Sat Oct 01, 2011 6:35 pm
- Forum: Number Theory
- Topic: smallest prime divisor
- Replies: 1
- Views: 1968
smallest prime divisor
find the smallest prime divisor of \[12^{2^{15}}+1\]
- Sat Sep 24, 2011 12:05 am
- Forum: International Mathematical Olympiad (IMO)
- Topic: iran mathematical olympiad
- Replies: 2
- Views: 2810
iran mathematical olympiad
if $a,b,c,d$ are natural numbers and $ab=cd$,then,prove that,$a+b+c+d$ cannot be a prime.
- Sat Sep 17, 2011 10:34 am
- Forum: Secondary Level
- Topic: Prove P is prime
- Replies: 7
- Views: 4978
Re: Prove P is prime
well,we know,if $p$ is not a prime,then it will have a prime divisor between $1$ and \[\sqrt{p}\] so, it will share a common factor with $(p-1)$ but not with $1$. so,$p$ cannot be a composite number.Hence,since it has to be a number(the question states that it does divide) so,it will be a prime numb...
- Sat Sep 17, 2011 10:24 am
- Forum: Number Theory
- Topic: For prime lovers
- Replies: 3
- Views: 2583
Re: For prime lovers
The period of the repeating decimal of $1/p$ is equal to the order of $10$ modulo $p$. If $10$ is a primitive root modulo $p$, the period is equal to $p − 1$; if not, the period is a factor of $p − 1$. This result can be deduced from Fermat's little theorem, which states that \[10^{p-1}\equiv 1(mod ...