1. Prove that if b and c are odd, then (a/bc)=(a/b)(a/c)
2. Prove that if a==b (mod c), where c is odd, then (a/c)=(b/c)
For odd number P=p_1*p_2*...*p_s, where p_k are primes, the jacobi symbol (d/P) is defined as (d/P)=(d/p_1)(d/p_2)...(d/p_s), where (d/p_k) is the legendre symbol mod p_k.
1. If b and c are odd, ...
Jacobi Symbols and Proofs are investigated. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.