### Proof of two Legendre Symbol identities

1) Use that (Z/pZ)* is cyclic to directly prove that (-3/p) = 1 when p = 1 (mod 3). 2) If p = 1 (mod 5), directly prove that (5/p) = 1. I know that with exercise 1, we show that there is an element c in (Z/pZ)* of order 3, and that (2c+1) ^2 = -3. Similarly for exercise 2, there is a c in (Z/pZ)* of order 5, and [(c + c