# Problem 504: Square on the Inside
Let ABCD be a quadrilateral whose vertices are lattice points lying on
the coordinate axes as follows: A(a, 0), B(0, b), C(−c, 0), D(0, −d),
where 1 ≤ a, b, c, d ≤ m and a, b, c, d, m are integers. It can be shown
that for m = 4 there are exactly 256 valid ways to construct ABCD. Of
these 256 quadrilaterals, 42 of them strictly contain a square number of
lattice points. How many quadrilaterals ABCD strictly contain a square
number of lattice points for m = 100?