Question 53
Let $k \neq 0$ be an integer. Prove that the number of ordered pairs $(x, y)$ of integers satisfying
$$
k = \frac{x^2 - xy + 2y^2}{x + y}
$$
is odd if and only if $k$ is divisible by $7$.
$$
k = \frac{x^2 - xy + 2y^2}{x + y}
$$
is odd if and only if $k$ is divisible by $7$.