Ononot — For any two positive integers x and y, they satisfy the equa

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Diophantine Equationseasy

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For any two positive integers $x$ and $y$ , they satisfy the equation $\\gcd(x, y) \\cdot \\operatorname{lcm}(x, y) = xy$ . Under what conditions does the related Diophantine equation $\\gcd(x, y) + \\operatorname{lcm}(x, y) = x + y$ hold?