Discussion on Bangladesh National Math Camp
-
Pro_GRMR
- Posts:46
- Joined:Wed Feb 03, 2021 1:58 pm
BdMO 2021 National Camp Discussion Thread
Unread post
by Pro_GRMR » Fri Apr 23, 2021 4:27 pm
Hey, Campers!
This thread's purpose is:-
Code: Select all
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.
Good Practices to follow:-
Code: Select all
1. Use [hide][/hide] to hide your hint/solution.
2. Describe what you're posting.
"When you change the way you look at things, the things you look at change." - Max Planck
-
Pro_GRMR
- Posts:46
- Joined:Wed Feb 03, 2021 1:58 pm
Unread post
by Pro_GRMR » 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-
"When you change the way you look at things, the things you look at change." - Max Planck
-
MrCriminal
- Posts:8
- Joined:Wed Mar 24, 2021 6:43 pm
Unread post
by MrCriminal » Fri Apr 23, 2021 4:53 pm
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 ):
-
Dustan - Posts:71
- Joined:Mon Aug 17, 2020 10:02 pm
Unread post
by Dustan » Fri Apr 23, 2021 5:17 pm
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-
- Attachments
-
- s1.jpg (27.96KiB)Viewed 4862 times
-
Pro_GRMR
- Posts:46
- Joined:Wed Feb 03, 2021 1:58 pm
Unread post
by Pro_GRMR » Fri Apr 23, 2021 6:59 pm
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:
"When you change the way you look at things, the things you look at change." - Max Planck
-
Anindya Biswas
- Posts:264
- Joined:Fri Oct 02, 2020 8:51 pm
- Location:Magura, Bangladesh
-
Contact:
Unread post
by Anindya Biswas » Fri Apr 23, 2021 9:21 pm
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.
"If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is."
— John von Neumann