$S$ is a set of all points $(a, b)$ such that $0 ≤ a$, $b ≤ k$. How many squares are there such that all the $4$ vertices are from set $S$?
For diagonal squares, a square must contain odd points on its side. so that we can join the mid points of each side. suppose we take $5$ points on each side, $5*5 will make = 1^{2}$ $3*3 will make = 3^{2}$ etc
so when $n$ is odd, its summation of all odd squares till $k$. & for even similar approach.
Can you guide me further? Please help.