# Jacobi Symbol Properties

1. Apr 15, 2010

### kingwinner

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 ($$a^2/n$$) = 1 = ($$a/n^2$$)
(ii) If gcd(ab,nm)=1, then ($$ab^2/nm^2$$)=(a/n)
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(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. Apr 17, 2010

### robert Ihnot

(a^2/n) = (a/n)(a/n). So what is it supposed to be?