3.2-3.2.1, due October 17

In the integral quadratic forms, I'm not sure what they mean by substituting integers other than (0, 0, 0, ..., 0) because I don't know where they're suggesting we substitute them. If it means for the ai's then how could it ever be something besides 0? I like theorem 3.2.1.1 because it gives us a general form we can use to find infinitely many pythagorean triples and it's not even that difficult to come up with. I hope that working with polynomials in this class works out better than it did in Abstract Algebra.