Given that x, y are positive integers with x as small as possible, and y minimized with that constraint, and x(x+1) | y(y+1), but neither x nor x+1 divides either y or y+1, find x^{2}+y^{2}.
Given that x, y are positive integers with x as small as possible, and y minimized with that constraint, and x(x+1) | y(y+1), but neither x nor x+1 divides either y or y+1, find x^{2}+y^{2}.