USSR MO

For students of class 9-10 (age 14-16)
Tahmid
Posts: 110
Joined: Wed Mar 20, 2013 10:50 pm

USSR MO

Unread post by Tahmid » Tue Jul 07, 2015 1:58 am

Let $n\geq 3 $ be an odd number . Show that there is a number in the set ,
{$ {2}^{1}-1,{2}^{2}-1,{2}^{3}-1,......,{2}^{n-1}-1 $}
which is divisible by n .

Tahmid
Posts: 110
Joined: Wed Mar 20, 2013 10:50 pm

Re: USSR MO

Unread post by Tahmid » Tue Jul 07, 2015 2:00 am

this is obvious by euler's theorem . :|
so , skip this and try in another way .

tanmoy
Posts: 289
Joined: Fri Oct 18, 2013 11:56 pm
Location: Rangpur,Bangladesh

Re: USSR MO

Unread post by tanmoy » Wed Jul 08, 2015 9:35 pm

I have got a solution using pigeonhole principle and contradiction. :geek:
"Questions we can't answer are far better than answers we can't question"

Tahmid
Posts: 110
Joined: Wed Mar 20, 2013 10:50 pm

Re: USSR MO

Unread post by Tahmid » Thu Jul 09, 2015 12:20 am

tanmoy wrote:I have got a solution using pigeonhole principle and contradiction. :geek:
actually i wanted that :)

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