Question 2
Let $T=\{(x,y)\in\mathbb Z^2:-20\le x,y\le20,\ (x,y)\ne(0,0)\}$. Color exactly one of $(x,y)$ and $(-x,-y)$ for every point of $T$. For a coloring, let $N$ be the number of ordered pairs of colored points $(x_1,y_1),(x_2,y_2)$ satisfying $x_1\equiv2x_2$ and $y_1\equiv2y_2\pmod {41}$. Determine all possible values of $N$.