Let S be the set of all the natural numbers, for which the line x/a+y/b=2 is a tangent to the curve (x/a)^n +(y/b)^n =2 at the point ( a, b ), ab ≠…

Let S be the set of all the natural numbers, for which the line $\displaystyle \frac{x}{\mathrm{a}}+\frac{y}{\mathrm{~b}}=2$ is a tangent to the curve $\displaystyle \left(\frac{x}{\mathrm{a}}\right)^{\mathrm{n}}+\left(\frac{y}{\mathrm{~b}}\right)^{\mathrm{n}}=2$ at the point $\displaystyle (\mathrm{a}, \mathrm{b}), \mathrm{ab} \neq 0$. Then: