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USSR MO

Posted: Tue Jul 07, 2015 1:58 am
by Tahmid
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 .

Re: USSR MO

Posted: Tue Jul 07, 2015 2:00 am
by Tahmid
this is obvious by euler's theorem . :|
so , skip this and try in another way .

Re: USSR MO

Posted: Wed Jul 08, 2015 9:35 pm
by tanmoy
I have got a solution using pigeonhole principle and contradiction. :geek:

Re: USSR MO

Posted: Thu Jul 09, 2015 12:20 am
by Tahmid
tanmoy wrote:I have got a solution using pigeonhole principle and contradiction. :geek:
actually i wanted that :)