Page 1 of 1
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.
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.
actually i wanted that