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 $100$?
BdMO National 2012: Junior 10
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)
(Important: Please make sure that you have read about the Rules, Posting Permissions and Forum Language)
- 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
\[100=2^2.5^2\]
We first get $25$ at $25^{th}$ term.That term is also divisible by $2^2$.So the answer is $25^{th}$ term.
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
Re: BdMO National 2012: Junior 10
Can you explain this logically?
- nafistiham
- Posts:829
- Joined:Mon Oct 17, 2011 3:56 pm
- Location:24.758613,90.400161
- Contact:
Re: BdMO National 2012: Jounior 10
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.
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.