BdMO National 2012: Junior 10

Discussion on Bangladesh Mathematical Olympiad (BdMO) National
User avatar
Zzzz
Posts: 172
Joined: Tue Dec 07, 2010 6:28 am
Location: 22° 48' 0" N / 89° 33' 0" E

BdMO National 2012: Junior 10

Unread post by Zzzz » Sun Feb 12, 2012 9:32 am

Problem 10:
The $n$-th term of a sequence is the least common multiple (l.c.m.) of the integers from $1$ to $n$. Which term of the sequence is the first one that is divisible by $100$?
Every logical solution to a problem has its own beauty.
(Important: Please make sure that you have read about the Rules, Posting Permissions and Forum Language)

User avatar
Phlembac Adib Hasan
Posts: 1016
Joined: Tue Nov 22, 2011 7:49 pm
Location: 127.0.0.1
Contact:

Re: BdMO National 2012: Junior 10

Unread post by Phlembac Adib Hasan » Sun Feb 12, 2012 10:49 pm

\[100=2^2.5^2\]
We first get $25$ at $25^{th}$ term.That term is also divisible by $2^2$.So the answer is $25^{th}$ term.
Welcome to BdMO Online Forum. Check out Forum Guides & Rules

Arafat
Posts: 5
Joined: Tue Feb 21, 2012 2:11 pm

Re: BdMO National 2012: Junior 10

Unread post by Arafat » Wed Mar 21, 2012 4:16 pm

Can you explain this logically?

User avatar
nafistiham
Posts: 829
Joined: Mon Oct 17, 2011 3:56 pm
Location: 24.758613,90.400161
Contact:

Re: BdMO National 2012: Jounior 10

Unread post by nafistiham » Thu Mar 22, 2012 1:24 am

He means to divide $100$ the term must divide $2^2,5^5$ the first term that divides $25$ is the $25^{th}$ term and it also divides $4$.That's why
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
Introduction:
Nafis Tiham
CSE Dept. SUST -HSC 14'
http://www.facebook.com/nafistiham
nafistiham@gmail

Post Reply