81. (10th grade) Determine the number $a$ so that the polynomial $x^{n} -a x^{n-1}+a x-1$ is divisible by $(x-1)^{2}$.
81. We divide the polynomial by $x-1$. In the obtained quotient, we substitute $x=1$ and set the result equal to zero. Then

$$
2+(1-a)(n-2)=0, \text { from which } a=\frac{n}{n-2}
$$