Representations by Quadratic Forms — Allen Hatcher
Mathematics — Number Theory · quadratic-forms-discriminant-representations
Problem
(a) Using quadratic reciprocity determine which primes are represented by some form of discriminant 17.
(b) Show that all forms of discriminant 17 are equivalent to the form x2+xy−4y2.
(c) Draw enough of the topograph of x2+xy−4y2 to show all values between −70 and 70, and verify that the primes that occur are precisely the ones predicted by your answer in part (a).