2017 Regional no.9 Dhaka

Forum rules
Please don't post problems (by starting a topic) in the "X: Solved" forums. Those forums are only for showcasing the problems for the convenience of the users. You can always 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.
Md. Rifat uddin
Posts:10
Joined:Thu Dec 15, 2016 1:32 pm
2017 Regional no.9 Dhaka

Unread post by Md. Rifat uddin » Sat Jun 03, 2017 5:08 pm

Anyone knows How to solve this ?? :/ :( :? :?
Attachments
Ashampoo_Snap_2017.06.03_17h01m25s_001_.jpg
Ashampoo_Snap_2017.06.03_17h01m25s_001_.jpg (77.79KiB)Viewed 10363 times

aritra barua
Posts:57
Joined:Sun Dec 11, 2016 2:01 pm

Re: 2017 Regional no.9 Dhaka

Unread post by aritra barua » Mon Jun 05, 2017 2:31 pm

Check the parity of the equation and the rest should be clear.

Md. Rifat uddin
Posts:10
Joined:Thu Dec 15, 2016 1:32 pm

Re: 2017 Regional no.9 Dhaka

Unread post by Md. Rifat uddin » Wed Jun 07, 2017 9:05 am

So there are no solutions?? But the powers of 2 can be negative,so how do I handle that??

User avatar
ahmedittihad
Posts:181
Joined:Mon Mar 28, 2016 6:21 pm

Re: 2017 Regional no.9 Dhaka

Unread post by ahmedittihad » Wed Jun 07, 2017 2:37 pm

No, there are solutions. You have to consider the case where $k+4-4m^2=0$ or $n^2+k-m^2=0$.
Frankly, my dear, I don't give a damn.

Md. Rifat uddin
Posts:10
Joined:Thu Dec 15, 2016 1:32 pm

Re: 2017 Regional no.9 Dhaka

Unread post by Md. Rifat uddin » Wed Jun 07, 2017 11:04 pm

Oh !! sorry I missed that case of k+n^2-m^2 =0. SO the ans. is 17 ?? :/

Zahin Hasin Rudro
Posts:11
Joined:Sun Jul 12, 2015 3:52 am

Re: 2017 Regional no.9 Dhaka

Unread post by Zahin Hasin Rudro » Thu Jun 08, 2017 1:00 am

I got 16 ,how 17 ??

Md. Rifat uddin
Posts:10
Joined:Thu Dec 15, 2016 1:32 pm

Re: 2017 Regional no.9 Dhaka

Unread post by Md. Rifat uddin » Thu Jun 08, 2017 3:05 pm

Actually I get 18 values .. I worked out the values of k- 15,21,27,33,35,39,51,55,57,77,99,65,69,85,87,93,95,81.

Zahin Hasin Rudro
Posts:11
Joined:Sun Jul 12, 2015 3:52 am

Re: 2017 Regional no.9 Dhaka

Unread post by Zahin Hasin Rudro » Fri Jun 09, 2017 1:49 am

Oops I missed 81and 93!

Md. Rifat uddin
Posts:10
Joined:Thu Dec 15, 2016 1:32 pm

Re: 2017 Regional no.9 Dhaka

Unread post by Md. Rifat uddin » Mon Jun 12, 2017 1:20 am

Btw I'm not sure id my ans. is correct :/ Am I correct??

User avatar
Abdullah Al Tanzim
Posts:24
Joined:Tue Apr 11, 2017 12:03 am
Location:Dhaka, Bangladesh.

Re: 2017 Regional no.9 Dhaka

Unread post by Abdullah Al Tanzim » Wed Jun 21, 2017 5:42 pm

I think the problem can be solved in this way--- 1+2^(4-3m^2-n^2)=2^(k+4-4m^2)+2^(n^2+k-m^2)
or,1+2^(4-3m^2-n^2)=2^k(2^(4-4m^2)+2^(n^2-m^2))
or,1+a/b=2^k(a+b)
or,(a+b)/b=2^k(a+b)
or,2^k=1/b
or,2^k=2^(m^2-n^2)
or,k=m^2-n^2
Then by solving this equation,I think the answer is 72

Post Reply