Exercise 8.2.1. Prove Euler's criterion for (a/p) = 1, by evaluating (p 1)! (mod p) as in the second part of proof #1, but now taking account of the solutions r (mod p) to r2 = a (mod p). Exercise 8.2.2. Let p be an odd prime. Explain how one can determine the integer (%) by knowing a P2 (mod p). (Euler's criterion gives a congruence, but here we are asking for the value of the integer (). Exercise 8.2.1. Prove Euler's criterion for (a/p) = 1, by evaluating (p 1)! (mod p) as in the second part of proof #1, but now taking account of the solutions r (mod p) to r2 = a (mod p). Exercise 8.2.2. Let p be an odd prime. Explain how one can determine the integer (%) by knowing a P2 (mod p). (Euler's criterion gives a congruence, but here we are asking for the value of the integer ()