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BdMO 2021 National Camp Discussion Thread
Posted: Fri Apr 23, 2021 4:27 pm
by Pro_GRMR
Hey, Campers!
This thread's purpose is:-
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1. To post our solutions to the problem sets. (Using Latex is easier this way)
2. To check each other's solutions and learn from them.
3. To share hints about the problems.
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1. Use [hide][/hide] to hide your hint/solution.
2. Describe what you're posting.
Example
Posted: Fri Apr 23, 2021 4:43 pm
by Pro_GRMR
This is an example.
I'm sharing a hint for problem 1 of IMO Prep Pset-1.
Problem-
Find, with proof, all positive integers $n$ for which $2^n+12^n+2011^n$ is a perfect square.
Hint-
Re: Example
Posted: Fri Apr 23, 2021 4:53 pm
by MrCriminal
Pro_GRMR wrote: ↑Fri Apr 23, 2021 4:43 pm
This is an example.
I'm sharing a hint for problem 1 of IMO Prep Pset-1.
Problem-
Find, with proof, all positive integers $n$ for which $2^n+12^n+2011^n$ is a perfect square.
Hint-
Finding the magic number is tough for newbies like me ):
Re: Example
Posted: Fri Apr 23, 2021 5:17 pm
by Dustan
Pro_GRMR wrote: ↑Fri Apr 23, 2021 4:43 pm
This is an example.
I'm sharing a hint for problem 1 of IMO Prep Pset-1.
Problem-
Find, with proof, all positive integers $n$ for which $2^n+12^n+2011^n$ is a perfect square.
Hint-
Re: Example
Posted: Fri Apr 23, 2021 6:59 pm
by Pro_GRMR
Dustan wrote: ↑Fri Apr 23, 2021 5:17 pm
MrCriminal wrote: ↑Fri Apr 23, 2021 4:53 pm
Finding the magic number is tough for newbies like me ):
This is how I did it:
Re: BdMO 2021 National Camp Discussion Thread
Posted: Fri Apr 23, 2021 9:21 pm
by Anindya Biswas
When $n>1$
First take mod $4$. It gives us $n$ even
Then consider mod $3$. It gives us $n$ odd
The rest should be clear.
Re: BdMO 2021 National Camp Discussion Thread
Posted: Sun Apr 25, 2021 10:44 am
by Asif Hossain
Next problem Pls
