This assignment is due next Thursday.

1. Use the law of quadratic reciprocity to compute (503/773) and (501/773). [I've written (x/y) for the Legendre symbol.] Note: 503 and 773 are prime. 501 isn't, even though my book says it is.

2. Decide whether 7 is a quadratic residue of 11 two ways: using the law of quadratic reciprocity and using Gauss' Lemma directly. Check your work by using brute force computation to find a square root or show that none exists.

3. Find all the primitive roots and all the quadratic residues of 5.

   Find all the primitive roots and all the quadratic residues of 17.

   State (and prove) generalizations about Fermat primes. (You can check your conjectures in part by looking at some of the residue classes mod 257, using the quadratic reciprocity law. You won't want to compute there exhaustively, though.)