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📰 Therefore, \(a = 2m\) is even, \(b = 2n\) is even, but \(m\) and \(n\) have opposite parity — so \(a + b = 2(m + n)\), \(b - a = 2(n - m)\) — wait, no:
📰 \(x = m + n\), \(y = n - m\) — both \(x, y\) are integers as long as \(m, n\) are integers. But \(m\) and \(n\) are integers with \(mn = 506\), so they can be any integer solution to \(mn = 506\).
📰 But since 506 is not a perfect square and has only 8 positive divisors, the number of integer solutions \((m, n)\) with \(mn = 506\) is exactly 16: for each divisor \(m\), \(n = 506/m\), and there are 16 such ordered pairs (including negatives).
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