that 1. If b=0 Let P be a prime, and b Z be such that gcd...

 

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that 1. If b=0 Let P be a prime, and b Z be such that gcd (b,pa) = p > 1. Prove (mod pa), then b is a quadratic residue modulo pa. 2. If 60 (mod pa) and s is odd, then b is not a quadratic residue modulo pa. 3. If 60 (mod pa) and s is even, then 6 is a quadratic residue modulo pa if and only if is a quadratic residue modulo p. b ps (Hint:) Write the binomial equation x = b (mod pa) and apply the method for the case when b is not invertible. that 1. If b=0 Let P be a prime, and b Z be such that gcd (b,pa) = p > 1. Prove (mod pa), then b is a quadratic residue modulo pa. 2. If 60 (mod pa) and s is odd, then b is not a quadratic residue modulo pa. 3. If 60 (mod pa) and s is even, then 6 is a quadratic residue modulo pa if and only if is a quadratic residue modulo p. b ps (Hint:) Write the binomial equation x = b (mod pa) and apply the method for the case when b is not invertible.