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📰 x = \frac{2m + 2n}{2} = m + n, \quad y = \frac{2n - 2m}{2} = n - m
📰 Each such pair yields an integer solution. Therefore, there are 16 lattice points.
📰 But note: each solution \((x, y)\) is counted once for each factor pair. Since \( (a,b) \) and \( (b,a) \) yield potentially different \((x,y)\), but in our setup \(a = x - y\), \(b = x + y\), so order matters in assignment. However, fixing \(a, b\) as both even and same parity already covers all valid factorizations.
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