Find all integers

For discussing Olympiad Level Number Theory problems
Marina19
Posts:28
Joined:Mon Sep 05, 2011 1:38 am
Find all integers

Unread post by Marina19 » Wed Nov 16, 2011 9:10 pm

Find all integers n>1 so that there are n points on the plane, from which every point lies outside the circle which contains all the other points and has it's centre in one of it.

Marina19
Posts:28
Joined:Mon Sep 05, 2011 1:38 am

Re: Find all integers

Unread post by Marina19 » Fri Nov 25, 2011 11:47 am

I know the answer is: It is possible if, and only if, 2|n. But please help me in proving that for n that is not divisible by 2, it is impossible.

Corei13
Posts:153
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Location:Chittagong

Re: Find all integers

Unread post by Corei13 » Fri Nov 25, 2011 2:08 pm

"from which every point lies outside the circle which contains all the other points and has it's centre in one of it.", I can't get it.
ধনঞ্জয় বিশ্বাস

Marina19
Posts:28
Joined:Mon Sep 05, 2011 1:38 am

Re: Find all integers

Unread post by Marina19 » Sat Nov 26, 2011 12:54 am

"from which every point lies outside the circle which contains all the other points and has it's centre in one of it.", I can't get it.
Let me describe it another way. We have n points on the plane and for every point we should be able to create a crircle which contains all the other points and has centre in one of these points so that every other point aparat from the chosen one is included in it.

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