Power of 2 is Difference between Two Powers
Jump to navigation
Jump to search
The validity of the material on this page is questionable.
This is so trivial I wonder whether something got lost in translation.
You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by resolving the issues.
Contents
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 $2$.
This is so trivial I wonder whether something got lost in translation.
You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by resolving the issues.
To discuss this proof in more detail, feel free to use the talk page.
If you are able to fix this page, then when you have done so you can remove this instance of {{Questionable}} from the code.
If you would welcome a second opinion as to whether your correction is correct, add a call to {{Proofread}} the page (see the proofread template for usage).
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
- $2^5 = 3^4 - 7^2$
Sources
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $32$
