A problem about number theory

Hey, I am sticked by a problem about number theory, i hope someone can give me some hints or steps on it.

Here is the problem, let p=2^n+1, show that n must be even.

And if p=2^n+1, and 3^((p-1)/2)=-1(mod p) show that p is a prime.

I tried to let when n is odd, p=2*2^k+1 and try to find the divisiors, but i failed

Also, for the second problem, i used the quardratic reciprocity law to do this problem but it seems not working.

Thanks for helping me guys!

Re: A problem about number theory

Quote:

Originally Posted by **ryancheng**

Hey, I am sticked by a problem about number theory, i hope someone can give me some hints or steps on it.

Here is the problem, let p=2^n+1, show that n must be even.

And if p=2^n+1, and 3^((p-1)/2)=-1(mod p) show that p is a prime.

I tried to let when n is odd, p=2*2^k+1 and try to find the divisiors, but i failed

Also, for the second problem, i used the quardratic reciprocity law to do this problem but it seems not working.

Thanks for helping me guys!

This has all the earmarks of a homework problem in a class on elementary number theory.

You need to do your own homework assignments.