Hasse-Minkowski Theorem for Quadratic Forms in Two and Three Variables
Phuc (Jerry) Ngo ’23, Can Tho, Vietnam
Majors: Computer Science; Mathematics
To determine the solvability of equations has been an extended and fundamental study in Mathematics. The local-global principle states two objects are equivalent globally if and only if they are equivalent locally at all places. By applying that principle, the Hasse - Minkowski theorem is able to tell the existence of rational solutions of an equation. This paper will explore the application of the Hasse-Minkowski Theorem for homogeneous quadratic forms in two and three variables using only undergraduate number theory. Some of the necessary proofs and definitions are provided. Moreover, programming codes for the Hasse-Minkowski theorem are also given at the end.