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 .

## USSR MO

### Re: USSR MO

this is obvious by euler's theorem .

so , skip this and try in another way .

so , skip this and try in another way .

### Re: USSR MO

I have got a solution using pigeonhole principle and contradiction.

"Questions we can't answer are far better than answers we can't question"

### Re: USSR MO

actually i wanted thattanmoy wrote:I have got a solution using pigeonhole principle and contradiction.