Hungery-1911/3 (BOMC-2)

sm.joty · Unread post by **sm.joty** » Wed Mar 28, 2012 12:35 pm

An one for you

Prove that,
$3^n+1$ is not divisible by $2^n $ for any integer $n$

Unread post by **SANZEED** » Wed Mar 28, 2012 1:45 pm

Vaia,I think $3^{n}+1$ is divisible by $2^{n}$ when $n=0,1$.So it is not true for all integers.

FahimFerdous · Unread post by **FahimFerdous** » Wed Mar 28, 2012 2:05 pm

Just taking mod 8 kills it.

FahimFerdous · Unread post by **FahimFerdous** » Wed Mar 28, 2012 2:06 pm

Yeah, Sanzeed is right. For n=0,1 it doesn't stand.

Unread post by **SANZEED** » Wed Mar 28, 2012 2:28 pm

Fahim vai,post the full solution,not necessarily formal...

Nadim Ul Abrar · Unread post by **Nadim Ul Abrar** » Wed Mar 28, 2012 2:55 pm

FahimFerdous · Unread post by **FahimFerdous** » Wed Mar 28, 2012 5:51 pm

Nadim's solution is same as mine.

Sazid Akhter Turzo · Unread post by **Sazid Akhter Turzo** » Wed Mar 28, 2012 7:04 pm

same as Fahim vaia.
Turzo

Unread post by **Phlembac Adib Hasan** » Thu Mar 29, 2012 11:19 am

Very easy.Same to Fahim vaia.

sm.joty · Unread post by **sm.joty** » Thu Mar 29, 2012 1:41 pm

I use induction. But Fahim & othrs method is quite easy than mine.

And for $n=0,1$ this relation is false. (this is not my fault.It is a fault of Hungarian Olympiad Committee

)

BdMO Online Forum