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