Does there exist a set
![M](/media/m/f/7/f/f7f312cf6ba459a332de8db3b8f906c4.png)
with the following properties?
(i) The set
![M](/media/m/f/7/f/f7f312cf6ba459a332de8db3b8f906c4.png)
consists of 1992 natural numbers.
(ii) Every element in
![M](/media/m/f/7/f/f7f312cf6ba459a332de8db3b8f906c4.png)
and the sum of any number of elements have the form
%V0
Does there exist a set $M$ with the following properties?
(i) The set $M$ consists of 1992 natural numbers.
(ii) Every element in $M$ and the sum of any number of elements have the form $m^k$ $(m, k \in \mathbb{N}, k \geq 2).$