I am looking for some interesting questions on quadratic residues. Anyone know of any resources for an elementary number theory course. I am not looking for drill problems to practice but some important results.
Starting with quadratic residue, I arrived at close-packing of spheres within 3 clicks on Wikipedia:
quadratic residue - quadratic reciprocity - cubic reciprocity - sphere packing.
Another example as for many number theoretic results is cryptography: quadratic-rest-problem.
I'm sure there are a lot more results which are probably more sophisticated, too.