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Number Theory

  1. Mar 14, 2010 #1
    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
     
  2. jcsd
  3. Mar 14, 2010 #2
    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
     
  4. Mar 15, 2010 #3
    That helped me a lot. Thanks a bunch :wink:
     
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