2017 Regional no.9 Dhaka
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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.
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.
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Anyone knows How to solve this ?? :/
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Re: 2017 Regional no.9 Dhaka
Check the parity of the equation and the rest should be clear.
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Re: 2017 Regional no.9 Dhaka
So there are no solutions?? But the powers of 2 can be negative,so how do I handle that??
- ahmedittihad
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Re: 2017 Regional no.9 Dhaka
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.
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Re: 2017 Regional no.9 Dhaka
Oh !! sorry I missed that case of k+n^2-m^2 =0. SO the ans. is 17 ?? :/
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Re: 2017 Regional no.9 Dhaka
I got 16 ,how 17 ??
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Re: 2017 Regional no.9 Dhaka
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.
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Re: 2017 Regional no.9 Dhaka
Oops I missed 81and 93!
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Re: 2017 Regional no.9 Dhaka
Btw I'm not sure id my ans. is correct :/ Am I correct??
- Abdullah Al Tanzim
- Posts:24
- Joined:Tue Apr 11, 2017 12:03 am
- Location:Dhaka, Bangladesh.
Re: 2017 Regional no.9 Dhaka
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
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