Division problem

Forum for the GRE subject test in mathematics.
brain
Posts: 28
Joined: Tue Aug 25, 2009 12:16 pm

Division problem

What is the remainder of $2^{125}$ divided by 13?

A 2 B 4 C 6 D 8 E 10

mdornbos
Posts: 27
Joined: Sun Sep 05, 2010 11:11 am

Re: Division problem

Use Fermat's Little Theorem. The answer should be C. 6.

The theorem is 2^(n-1)=1 mod n.

So 2^(12)=1 mod 13.

Now 2^125=2^(12*10)*2^(5)=2^(5)=32=6 mod 13.

brain
Posts: 28
Joined: Tue Aug 25, 2009 12:16 pm

Thanks.