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