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Jacobi Symbols and Proofs

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)

Solution Preview

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, ...

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