Question 118
For any two numbers $x, y$, we denote $N(x, y) = x^2 - xy + y^2$.
a. Prove the product formula $N(a, b)N(x, y) = N(ax - by, ay + bx - by)$.
b. Show that the equation $N(x, y) = 2023 - 490z^2$ has at least 16 distinct solution triples $(x, y, z)$ with integers $x, y, z \ge 0$.
a. Prove the product formula $N(a, b)N(x, y) = N(ax - by, ay + bx - by)$.
b. Show that the equation $N(x, y) = 2023 - 490z^2$ has at least 16 distinct solution triples $(x, y, z)$ with integers $x, y, z \ge 0$.