• Use the Quadratic Reciprocity Law to find a congruence describing all primes for which 5 is a

quadratic residue. In other words, characterize all primes p for which (5/p) = 1.

[Hint: There are two cases to consider when p 1 (mod 4) and then when p 3 (mod 4). In the first case the Quadratic Reciprocity Law will tell you that (p/5) = (5/p). Determine the values of p (mod 5) for which this equals 1, and then calculate the values modulo 20 for which both conditions hold. Do the same in the second case and combine your answers