Number Theory

  • Thread starter ak_89
  • Start date
  • #1
ak_89
5
0
I was just working on some problems from a text book 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
 

Answers and Replies

  • #2
Petek
Gold Member
393
15
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
 
  • #3
ak_89
5
0
That helped me a lot. Thanks a bunch :wink:
 

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