2018 Putnam B3

Find all positive integers $n < 10^{100}$ for which simultaneously $n$ divides $2^n$, $n-1$ divides $2^n-1$,

and $n-2$ divides $2^n - 2$.

查找所有正整数 $n < 10^{100}$，同时 $n$ 除以 $2^n$，$n-1$ 除以 $2^n-1$，

$n-2$ 除以 $2^n - 2$。