# Power of 2 is Difference between Two Powers

## Theorem

Let $n \in \Z_{>0}$ be a power of $2$.

Then $n$ is the difference between powers of two positive integers greater than or equal to $2$.

## Proof

$2^k = 2^{k+1} - 2^k$

$\blacksquare$

## Examples

### $2^0$ expressed as Difference between Two Powers

$2^0 = 3^2 - 2^3$

### $2^1$ expressed as Difference between Two Powers

$2^1 = 3^3 - 5^2$

### $2^2$ expressed as Difference between Two Powers

$2^2 = 5^3 - 11^2$

### $2^4$ expressed as Difference between Two Powers

$2^4 = 5^2 - 3^2$

### $2^5$ expressed as Difference between Two Powers

$2^5 = 3^4 - 7^2$