This is a theorem about Jacobi symbols in my textbook:(adsbygoogle = window.adsbygoogle || []).push({});

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!

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Jacobi Symbol Properties

**Physics Forums | Science Articles, Homework Help, Discussion**