Q:

Expressing positive Integers as a sum of 2

Can we express any positive integer larger than $2$ as ($2^{n}+$ some number other than $1$ ) ? Or say, (lots of $2s+$ some number other than $1$)? Except $3$ is special case, of course.

A:

Let $p>3$ be given
$$p=2^{1}+(p-2) \quad \blacksquare$$
Additionally, if $n$ is not restricted to the natural numbers, you can get $3$ by $3=2^{0}+2$

