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More Number Theory

  1. Mar 15, 2010 #1
    I have a few questions I am having troubles with. If someone can push me in the right direction that would be awesome. Here are the questions:

    1. Prove that the prime divisors, p cannot equal 3, of the integer n2-n+1 have the form 6k+1. (Hint: turn this into a statement about (-3/p) )

    2. Show that if p is congruent to 1 (mod 4), then x2 is congruent to -1 (mod p) has a solution given by the least residue (mod p) of ( (p-1)/2)!

    I honestly have no idea how to start. I would greatly appreciate some help.
  2. jcsd
  3. Mar 17, 2010 #2
    For the first question, try multiplying the n2-n+1 term by some integer and rearranging things...

    Unfortunately, I'm stumped on how to do the second question :uhh:
  4. Mar 18, 2010 #3
    Thanks! I got that proof. But I am still stuck on the second question as well. I played around with it.. but I have yet to get anywhere that is useful to prove the question.

    I could really use some help.
  5. Mar 18, 2010 #4
    Hint for #2: Use Wilson's Theorem.

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