Proving 3 as a Quadratic Non-Residue of Mersenne Primes | Number Theory Problem

[ak_89]

I was just working on some problems from a textbook I own (for fun).
I am not sure how to start this problem at all.

Here's the question: Show that 3 is a quadratic non-residue of all Mersenne primes greater than 3.

I honestly don't know how to start. If I could get some help to push me in the right direction that would be great.

Thanks

 

[Petek]

Do you know the law of quadratic reciprocity? If so, use it to work out examples for small Mersenne primes and look for some patterns.

Petek

 

[ak_89]

That helped me a lot. Thanks a bunch