Dhaka Secondary 2011/2 (Junior 2011/4)

Problem for Secondary Group from Divisional Mathematical Olympiad will be solved here.
Forum rules
Please don't post problems (by starting a topic) in the "Secondary: Solved" forum. This forum is only for showcasing the problems for the convenience of the users. You can post the problems in the main Divisional Math Olympiad forum. Later we shall move that topic with proper formatting, and post in the resource section.
BdMO
Posts: 134
Joined: Tue Jan 18, 2011 1:31 pm

Dhaka Secondary 2011/2 (Junior 2011/4)

Unread post by BdMO » Fri Jan 28, 2011 9:44 pm

$A$ is the product of seven odd prime numbers. $A \times B$ is a perfect even square. What is the minimum number of prime factors of $B$?

Hasib
Posts: 238
Joined: Fri Dec 10, 2010 11:29 am
Location: খুলনা, বাংলাদেশ
Contact:

Re: Dhaka Secondary 2011/2

Unread post by Hasib » Fri Jan 28, 2011 10:04 pm

are the seven odd prime numbers distinct?
A man is not finished when he's defeated, he's finished when he quits.

User avatar
Avik Roy
Posts: 156
Joined: Tue Dec 07, 2010 2:07 am

Re: Dhaka Secondary 2011/2

Unread post by Avik Roy » Fri Jan 28, 2011 11:33 pm

yes, they are distinct
"Je le vois, mais je ne le crois pas!" - Georg Ferdinand Ludwig Philipp Cantor

Hasib
Posts: 238
Joined: Fri Dec 10, 2010 11:29 am
Location: খুলনা, বাংলাদেশ
Contact:

Re: Dhaka Secondary 2011/2

Unread post by Hasib » Fri Jan 28, 2011 11:46 pm

then the ans is 8.
Let, $A=p_1.p_2...p_7$ none of them are same or 2. So $B=2.2.p_1.p_2...p_7$ then the ans is 8 ;)
A man is not finished when he's defeated, he's finished when he quits.

Shifat
Posts: 53
Joined: Sun Jul 31, 2011 12:21 pm
Location: Dhaka, Bangladesh

Re: Dhaka Secondary 2011/2 (Junior 2011/4)

Unread post by Shifat » Fri Aug 05, 2011 2:55 am

bro i did not get your solution, can u describe it even more clearly??@hasib bro

User avatar
amlansaha
Posts: 100
Joined: Tue Feb 08, 2011 1:11 pm
Location: Khulna, Bangladesh
Contact:

Re: Dhaka Secondary 2011/2 (Junior 2011/4)

Unread post by amlansaha » Wed Nov 30, 2011 12:46 pm

shifat, i am giving an example. suppose $A= 3\times 5\times 7\times 11\times 13\times 17\times 19$ and as $A\times B$ is an even perfect square, it should look like this $A\times B= 2^2\times 3^2\times 5^2\times 7^2\times 11^2\times 13^2\times 17^2\times 19^2\times $(any other perfect square) . thus we get $B=2^2\times 3\times 5\times 7\times 11\times 13\times 17\times 19\times $(any other perfect square). so the minimum prime factors of $B$ are $2$, $3$, $5$, $7$, $11$, $13$, $17$, $19$. so the answer is $8$. Hasib has just used $p_{1}$, $ p_{2}$, $ p_{3} $..... in lieu of $3$, $5$, $7$.... that's it :D
অম্লান সাহা

Shifat
Posts: 53
Joined: Sun Jul 31, 2011 12:21 pm
Location: Dhaka, Bangladesh

Re: Dhaka Secondary 2011/2 (Junior 2011/4)

Unread post by Shifat » Sun Dec 18, 2011 1:46 am

oh, got it, thanks.....:D

Naheed
Posts: 20
Joined: Sun Dec 16, 2012 11:10 pm

Re: Dhaka Secondary 2011/2 (Junior 2011/4)

Unread post by Naheed » Thu Jan 07, 2016 2:58 pm

What's a perfect even square?

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

Re: Dhaka Secondary 2011/2 (Junior 2011/4)

Unread post by Phlembac Adib Hasan » Sun Jan 10, 2016 4:34 pm

Perfect even squares = The squares of even numbers.
Welcome to BdMO Online Forum. Check out Forum Guides & Rules

Post Reply