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Proof about number theory

  1. Sep 28, 2009 #1
    Recall the definition of n! (read n factorial"):
    n! = (n)(n-1)(n-2) ….(2)(1) =∏(k)
    In both (a) and (b) below, suppose p≥3 is prime.
    (a) Prove that if x∈ Zpx is a solution to x square ≡1 (mod p), then x ≡±1 (mod p).
    (b) Prove that (p-1)!≡±1 (mod p)

    Zpx x shoud be above p

    a and b looks like some theorem proof
     
  2. jcsd
  3. Sep 29, 2009 #2

    MathematicalPhysicist

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    Gold Member

    Hints:
    1. factorise x^2-1=(x-1)(x+1).

    2. this theorem is called wilson theorem.
     
  4. Oct 2, 2009 #3
    Hint: (2) can be looked at as a case of a and its inverse. The first part, (1) plays a special role in that.
     
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