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Jacobi Symbol Properties

  1. Apr 15, 2010 #1
    This is a theorem about Jacobi symbols in my textbook:
    Let n and m be ODD and positive. Then (a/nm)=(a/n)(a/m) and (ab/n)=(a/n)(b/n)
    Moreover,
    (i) If gcd(a,n)=1, then ([tex]a^2/n[/tex]) = 1 = ([tex]a/n^2[/tex])
    (ii) If gcd(ab,nm)=1, then ([tex]ab^2/nm^2[/tex])=(a/n)
    =====================================

    (i) is easy and follows from the definition, but how can we prove (ii)? My textbook stated the theorem without proof and just says the proofs are easy, but I have no idea why (ii) is true.

    Any help is appreciated!
     
  2. jcsd
  3. Apr 17, 2010 #2
    (a^2/n) = (a/n)(a/n). So what is it supposed to be?
     
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